Showing papers by "Young Jin Suh published in 2014"
TL;DR: In this paper, the authors introduced the notion of shape operator of Codazzi type for real hypersurfaces in the complex quadric Qm = SOm+2/SOmSO2.
Abstract: First, we introduce the notion of shape operator of Codazzi type for real hypersurfaces in the complex quadric Qm = SOm+2/SOmSO2. Next, we give a complete proof of non-existence of real hypersurfaces in Qm = SOm+2/SOmSO2 with shape operator of Codazzi type. Motivated by this result we have given a complete classification of real hypersurfaces in Qm = SOm+2/SOmSO2 with Reeb parallel shape operator.
66 citations
Posted Content•
TL;DR: In this paper, the authors classify real hypersurfaces with Reeb invariant shape operator in complex hyperbolic two-plane Grassmannians and show that a tube over a totally geodesic manifold becomes a horosphere when the center at infinity is singular and of type JN \in {\mathfrak J}N$ for a unit normal vector field.
Abstract: We classify all of real hypersurfaces $M$ with Reeb invariant shape operator in complex hyperbolic two-plane Grassmannians $SU_{2,m}/S(U_2{\cdot}U_m)$, $m \geq 2$. Then it becomes a tube over a totally geodesic $SU_{2,m-1}/S(U_2{\cdot}U_{m-1})$ in $SU_{2,m}/S(U_2{\cdot}U_m)$ or a horosphere whose center at infinity is singular and of type $JN \in {\mathfrak J}N$ for a unit normal vector field $N$ of $M$.
58 citations
TL;DR: In this paper, it was shown that there is no Hopf real hypersurface in complex hyperbolic two-plane Grassmannians with parallel Ricci tensor, and therefore, there does not exist any hopf real surface in the Grassmannian.
Abstract: In this paper we prove that there does not exist any Hopf real hypersurface in complex hyperbolic two-plane Grassmannians with parallel Ricci tensor.
40 citations
TL;DR: In this paper, it was shown that the integral curves of the gradient field are geodesics and that the scalar field satisfies a generalized eikonal equation, and the Petrov classification of pseudo-Z symmetric space-time manifolds was investigated.
Abstract: In this paper, we investigate Pseudo-Z symmetric space-time manifolds. First, we deal with elementary properties showing that the associated form Ak is closed: in the case the Ricci tensor results to be Weyl compatible. This notion was recently introduced by one of the present authors. The consequences of the Weyl compatibility on the magnetic part of the Weyl tensor are pointed out. This determines the Petrov types of such space times. Finally, we investigate some interesting properties of (PZS)4 space-time; in particular, we take into consideration perfect fluid and scalar field space-time, and interesting properties are pointed out, including the Petrov classification. In the case of scalar field space-time, it is shown that the scalar field satisfies a generalized eikonal equation. Further, it is shown that the integral curves of the gradient field are geodesics. A classical method to find a general integral is presented.
40 citations
TL;DR: In this paper, the notion of recurrent conformal 2-forms on a pseudo-Riemannian manifold of arbitrary signature was introduced, and it was shown that the Ricci tensor is Riemann compatible or equivalently, Weyl compatible.
Abstract: In this paper, we introduce the notion of recurrent conformal 2-forms on a pseudo-Riemannian manifold of arbitrary signature. Some theorems already proved for the same differential structure on a Riemannian manifold are proven to hold in this more general contest. Moreover other interesting results are pointed out; it is proven that if the associated covector is closed, then the Ricci tensor is Riemann compatible or equivalently, Weyl compatible: these notions were recently introduced and investigated by one of the present authors. Further some new results about the vanishing of some Weyl scalars on a pseudo-Riemannian manifold are given: it turns out that they are consequence of the generalized Derdzinski–Shen theorem. Topological properties involving the vanishing of Pontryagin forms and recurrent conformal 2-forms are then stated. Finally, we study the properties of recurrent conformal 2-forms on Lorentzian manifolds (space-times). Previous theorems stated on a pseudo-Riemannian manifold of arbitrary signature are then interpreted in the light of the classification of space-times in four or in higher dimensions.
33 citations
TL;DR: It is shown that such a hypersurface must be a tube over a totally real totally geodesic HH^n, m=2n, in the noncompact complex two-plane Grassmannian SU(2,m)/S(U(2)@?U(m), a horosphere whose center at the infinity is singular or an exceptional case.
26 citations
TL;DR: Similar to IDC patients, molecular subtype should be considered when determining the prognosis and treatment regimen for ILC patients.
Abstract: To investigate the clinicopathological characteristics and the survival outcomes of invasive lobular carcinoma (ILC) patients compared to invasive ductal carcinoma (IDC) patients according to their molecular subtype We compared the clinicopathological characteristics, breast cancer-specific survival (BCSS) and overall survival (OS) between patients with IDC (n = 14,547) and ILC (n = 528) The ILC presented with a larger tumor size, more advanced cancer stage, increased rate of hormonal receptor positivity, human epidermal growth factor 2 (HER2) negativity and mastectomy than the IDC The ILC patients more frequently presented with the luminal A subtype, whereas the IDC patients more frequently presented with the luminal B, HER2-overexpression, or triple negative subtype The BCSS and OS were not significantly different between the IDC and ILC for each molecular subtype Similar to IDC patients, molecular subtype should be considered when determining the prognosis and treatment regimen for ILC patients
23 citations
TL;DR: It is suggested that weight gain after adjuvant TAC chemotherapy is common in Korean women with breast cancer, and in contrast to previous Western studies, weight gain did not appear to be sustained, and there was no relationship between weight gain and poor RFS.
Abstract: The aim of this study was to characterize weight changes and analyze their effect on prognosis after three-drug combination chemotherapy using docetaxel, doxorubicin and cyclophosphamide (TAC) chemotherapy in Korean women with breast cancer. We analyzed weight changes and the effect of these changes on relapse-free survival (RFS) in 108 patients who received adjuvant TAC chemotherapy at the Department of Surgery of St. Vincent's Hospital at the Catholic University of Korea between January 2005 and March 2010. Following chemotherapy, 59 (54.6%) patients experienced weight gain, with their weight significantly increasing compared to their weight at diagnosis (p<0.0001). However, weight gain after chemotherapy was not associated with RFS [hazard ratio (HR) 1.1; 95% confidence interval (CI) 0.4-3.0; p=0.8955]. No significant weight (at 12 months, p=0.522; at 24 months, p=0.632) and body mass index (BMI) (at 12 months, p=0.381; at 24 months, p=0.288) changes were observed compared to the weight and BMI at diagnosis, and weight change at 12 months (HR 1.9; 95% CI 0.6-6.1; p=0.2786) and 24 months (HR 2.7; 95% CI 0.9-8.4; p=0.0776) was not associated with RFS. The present study suggests that weight gain after adjuvant TAC chemotherapy is common in Korean women with breast cancer. In contrast to previous Western studies, weight gain did not appear to be sustained, and there was no relationship between weight gain and poor RFS.
21 citations
TL;DR: In this article, non-existence theorems for Hopf hypersurfaces in complex two-plane Grassmannians were shown for the case where the distribution of the Reeb vector field is invariant by shape operator.
Abstract: In this paper, we give non-existence theorems for Hopf hypersurfaces in complex two-plane Grassmannians $$G_2(\mathbb{C }^{m+2})$$
with $$\mathfrak D $$
-parallel normal Jacobi operator $${\bar{R}}_N$$
and $$\mathfrak D $$
-parallel structure Jacobi operator $$R_{\xi }$$
if the distribution $$\mathfrak D $$
or $$\mathfrak D ^{\bot }$$
component of the Reeb vector field is invariant by the shape operator, respectively.
15 citations
TL;DR: In this paper, a new notion of pseudo anti-commuting for real hypersurfaces in complex two-plane Grassmannians G 2 (C m + 2 ) was introduced and a complete classification theorem was proved.
13 citations
TL;DR: Radiotherapy using TomoDirect in early breast cancer patients showed acceptable toxicities and optimal results in terms of target coverage and organ at risk sparing.
Abstract: To evaluate the technical feasibility and toxicity of TomoDirect in breast cancer patients who received radiotherapy after breast-conserving surgery. 155 consecutive patients with breast carcinoma in situ or T1-2 breast cancer with negative lymph node received breast irradiation with TomoDirect using simultaneous integrated boost technique in the prospective cohort study. A radiation dose of 50.4 Gy and 57.4 Gy in 28 fractions was prescribed to the ipsilateral breast and tumor bed, respectively. Dosimetric parameters of target and organ at risk and acute complication were assessed prospectively. The mean dose for the tumor bed is 58.90 Gy. The mean values of V54.53Gy (95% of the prescribed dose), V63.14Gy (110% of the prescribed dose), and V66.01Gy (115% of the prescribed dose) were 99.97%, 1.26%, and 0%, respectively. The mean value of radiation conformality index was 1.01. The mean value of radical dose homogeneity index was 0.89. The average dose irradiated to the ipsilateral lung, heart, and contralateral breast was 4.72 Gy, 1.09 Gy, and 0.19 Gy, respectively. The most common toxicity was dermatitis. During breast irradiation, grade 2 and 3 dermatitis occurred in 41 (26.5%) and 6 (3.9%) of the 155 patients, respectively. Two patients had arm lymphedema during breast irradiation. Two patients had grade 2 pneumonitis 1 month after breast irradiation. Radiotherapy using TomoDirect in early breast cancer patients showed acceptable toxicities and optimal results in terms of target coverage and organ at risk sparing.
01 Jan 2014
TL;DR: In this paper, a new notion of recurrent structure Jacobi operator was introduced for tangent vector fields X and Y on a real hypersurface M in a complex two-plane Grassmannian.
Abstract: In this paper, we introduce a new notion of recurrent structure Jacobi operator, that is, \((
abla _{X}R_{\xi })Y =\omega (X)R_{\xi }Y\) for any tangent vector fields X and Y on a real hypersurface M in a complex two-plane Grassmannian, where R ξ denotes the structure Jacobi operator and ω a certain 1-form on M. Next, we prove that there does not exist any Hopf hypersurface M in a complex two-plane Grassmannian with recurrent structure Jacobi operator.
TL;DR: In this paper, a rigidity theorem of the complex hyperbolic space C H m with respect to volume entropy has been derived from geometrical study of horospheres, among asymptotically harmonic Hadamard manifolds.
Abstract: From geometrical study of horospheres we obtain, among asymptotically harmonic Hadamard manifolds, a rigidity theorem of the complex hyperbolic space C H m with respect to volume entropy. We also characterize C H m horospherically in terms of holomorphic curvature boundedness. Corresponding quaternionic analogues are obtained.
TL;DR: In this article, a new commuting condition in relation to the shape operator A and a new operator φφ 1 induced by two structure tensors φ and φ 1 was proposed.
Abstract: Lee, Kim and Suh (2012) gave a characterization for real hypersurfaces M of Type (A) in complex two plane Grassmannians G 2(ℂ m+2) with a commuting condition between the shape operator A and the structure tensors φ and φ 1 for M in G 2(ℂ m+2). Motivated by this geometrical notion, in this paper we consider a new commuting condition in relation to the shape operator A and a new operator φφ 1 induced by two structure tensors φ and φ 1. That is, this commuting shape operator is given by φφ 1 A = A φφ 1. Using this condition, we prove that M is locally congruent to a tube of radius r over a totally geodesic G 2(ℂ m+1) in G 2(ℂ m+2).
TL;DR: In this article, a characterization of a real hypersurface of Type in complex two-plane Grassmannians is given by means of the Reeb parallel structure Jacobi operator.
Abstract: In this paper we give a characterization of a real hypersurface of Type in complex two-plane Grassmannians , which means a tube over a totally geodesic in , by means of the Reeb parallel structure Jacobi operator .
Posted Content•
TL;DR: In this article, a new notion of generalized Tanaka-Webster Reeb parallel Ricci tensor for real hypersurfaces in complex two-plane Grassmannians was introduced.
Abstract: There are several kinds of classification problems for real hypersurfaces in complex two-plane Grassmannians $G_2({\mathbb C}^{m+2})$. Among them, Suh classified Hopf hypersurfaces $M$ in $G_2({\mathbb C}^{m+2})$ with Reeb parallel Ricci tensor in Levi-Civita connection. In this paper, we introduce a new notion of generalized Tanaka-Webster Reeb parallel Ricci tensor for $M$ in $G_2({\mathbb C}^{m+2})$. By using such parallel conditions, we give complete classifications of Hopf hypersurfaces in $G_2({\mathbb C}^{m+2})$.
TL;DR: In this paper, the generalized Tanaka-Webster connection was considered for a real hypersurface in a complex two-plane Grassmannian, where m = 2n and where m is 2n.
Abstract: Regarding the generalized Tanaka-Webster connection, we considered a new notion of $$\mathfrak{D}^ \bot$$
-parallel structure Jacobi operator for a real hypersurface in a complex two-plane Grassmannian G
2(ℂ
m+2) and proved that a real hypersurface in G
2(ℂ
m+2) with generalized Tanaka-Webster $$\mathfrak{D}^ \bot$$
-parallel structure Jacobi operator is locally congruent to an open part of a tube around a totally geodesic quaternionic projective space ℍP
n
in G
2(ℂ
m+2), where m = 2n.
01 Jan 2014
TL;DR: In this paper, the shape operator and the structure Jacobi operator on real hypersurfaces were studied and the commutativity properties of these operators with the shape operators were investigated.
Abstract: Let M be a real hypersurface in complex projective space. On M we have the Levi-Civita connection and for any nonzero constant k the corresponding generalized Tanaka-Webster connection. For such a k and any vector field X tangent to M we can define from both connections the kth Cho operator F X (k). We study commutativity properties of these operators with the shape operator and the structure Jacobi operator on M obtaining some characterizations of either Type (A) real hypersurfaces or ruled real hypersurfaces.
Posted Content•
TL;DR: In this paper, the authors considered a new commuting condition, that is, the restricted Jacobi operator S = S (R_\xi\phi) S =S (Bar{R}_N\phi$ ) big (resp.
Abstract: In this paper, we have considered a new commuting condition, that is, $(R_\xi\phi) S = S (R_\xi\phi)$ \big(resp. $(\Bar{R}_N\phi) S = S (\Bar{R}_N\phi$)\big) between the restricted Jacobi operator~$R_\xi\phi$ (resp. $\Bar{R}_N\phi$), and the Ricci tensor $S$ for real hypersurfaces $M$ in $G_2({\mathbb C}^{m+2})$. In terms of this condition we give a complete classification for Hopf hypersurfaces $M$ in $G_2({\mathbb C}^{m+2})$.
TL;DR: In this paper, the authors characterize geodesic hyperspheres of radius r such that cot2(r)=\frac{1}{2} as the unique real hypersurfaces in complex projective space whose structure Jacobi operator satisfies a pair of conditions.
Abstract: We characterize geodesic hyperspheres of radius r such that cot2(r)=\frac{1}{2} as the unique real hypersurfaces in complex projective space whose structure Jacobi operator satisfies a pair of conditions.
TL;DR: In this article, the authors introduced some notions of invariancy for the Ricci tensor on real hypersurfaces in complex two-plane Grassmannians G 2 (C m + 2 ), namely, F -invariant and invariant R tensor.
01 Jan 2014
TL;DR: Suh et al. as mentioned in this paper classified real hypersurfaces with isometric Reeb flow in complex hyperbolic two-plane Grassmannian and gave another characterization for these model spaces by the Reeb invariant shape operator.
Abstract: A main objective in submanifold geometry is the classification of homogeneous hypersurfaces. Homogeneous hypersurfaces arise as principal orbits of cohomogeneity one actions, and so their classification is equivalent to the classification of cohomogeneity one actions up to orbit equivalence. Actually, the classification of cohomogeneity one actions in irreducible simply connected Riemannian symmetric spaces of rank 2 of noncompact type was obtained by J. Berndt and Y.J. Suh (for complex hyperbolic two-plane Grassmannian \(SU_{2,m}/S(U_{2}\cdot U_{m}\)), (Berndt and Suh, Int. J. Math. 23, 1250103 (35pages), 2012)). From this classification, in (Suh, Adv. Appl. Math. 50, 645–659, 2013) Suh classified real hypersurfaces with isometric Reeb flow in \(SU_{2,m}/S(U_{2}\cdot U_{m})\), m ≥ 2. Each one can be described as a tube over a totally geodesic \(SU_{2,m-1}/S(U_{2}\cdot U_{m-1})\) in \(SU_{2,m}/S(U_{2}\cdot U_{m})\) or a horosphere whose center at infinity is singular. By using this result, we want to give another characterization for these model spaces by the Reeb invariant shape operator, that is, \(\mathcal{L}_{\xi }A = 0\).
TL;DR: In this article, a new notion of generalized Tanaka-Webster Reeb Reeb recurrent Ricci tensor tensor in complex two-plane Grassmannians was introduced and a non-existence property for real hypersurfaces with such a condition was given.
Abstract: In this paper, we have introduced a new notion of generalized Tanaka-Webster Reeb recurrent Ricci tensor in complex two-plane Grassmannians $G_2({\mathbb C}^{m+2})$. Next, we give a non-existence property for real hypersurfaces $M$ in $G_2({\mathbb C}^{m+2})$ with such a condition.
Posted Content•
TL;DR: In this article, the authors prove the non-existence of Hopf real hypersurfaces in complex two-plane Grassmannians whose Ricci tensor is parallel with respect to the generalized Tanaka-Webster connection.
Abstract: We prove the non-existence of Hopf real hypersurfaces in complex two-plane Grassmannians whose Ricci tensor is parallel with respect to the generalized Tanaka-Webster connection.
01 Jan 2014
TL;DR: In this article, a new notion of parallel Jacobi operator for real hypersurfaces in complex two-plane Grassmannians was proposed, and the generalized Tanaka-Webster connection was considered.
Abstract: In relation to the generalized Tanaka-Webster connection, we consider a new notion of parallel Jacobi operator for real hypersurfaces in complex two-plane Grassmannians \(G_{2}(\mathbb{C}^{m+2})\) and show results about real hypersurfaces in \(G_{2}(\mathbb{C}^{m+2})\) with generalized Tanaka-Webster parallel structure Jacobi operator and normal Jacobi operator.
Posted Content•
TL;DR: Using generalized Tanaka-Webster connection, the authors considered a real hypersurface in a complex two-plane Grassmannian and proved that it is an open part of a tube around a totally geodesic.
Abstract: Using generalized Tanaka-Webster connection, we considered a real hypersurface $M$ in a complex two-plane Grassmannian $G_2({\mathbb C}^{m+2})$ when the GTW Reeb Lie derivative of the structure Jacobi operator coincides with the Reeb Lie derivative. Next using the method of simultaneous diagonalization, we prove a complete classification for a real hypersurface in $G_2({\mathbb C}^{m+2})$ satisfying such a condition. In this case, we have proved that $M$ is an open part of a tube around a totally geodesic $G_2({\mathbb C}^{m+1})$ in $G_2({\mathbb C}^{m+2})$.
Posted Content•
TL;DR: In this article, the curvature tensor of a real hypersurface in complex hyperbolic two-plane Grassmannians was derived from the equation of Gauss and a new Ricci tensor was derived.
Abstract: In this paper we first introduce the full expression of the curvature tensor of a real hypersurface $M$ in complex hyperbolic two-plane Grassmannians $SU_{2,m}/S(U_2{\cdot}U_m)$, $m{\ge}2$ from the equation of Gauss. Next we derive a new formula for the Ricci tensor of $M$ in $SU_{2,m}/S(U_2{\cdot}U_m)$. Finally we give a complete classification of Hopf hypersurfaces in complex hyperbolic two-plane Grassmannians $SU_{2,m}/S(U_2{\cdot}U_m)$ with commuting Ricci tensor. Each can be described as a tube over a totally geodesic $SU_{2,m-1}/S(U_2{\cdot}U_{m-1})$ in $SU_{2,m}/S(U_2{\cdot}U_m)$ or a horosphere whose center at infinity is singular.