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Tatsuyoshi Hamada

Other affiliations: Nihon University
Bio: Tatsuyoshi Hamada is an academic researcher from Fukuoka University. The author has contributed to research in topics: Ricci curvature & Mathematical software. The author has an hindex of 5, co-authored 17 publications receiving 124 citations. Previous affiliations of Tatsuyoshi Hamada include Nihon University.

Papers
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Journal ArticleDOI
TL;DR: In this article, a characterization of pseudo-Einstein real hypersurfaces of quaternionic projective spaces is given by using an estimate of the length of the Ricci tensor S, which is a quaternion version of a result of Kimura and Maeda.
Abstract: Let HPn be a quaternionic projective space, n = 3, with metric G of constant quaternionic sectional curvature 4, and let M be a connected real hypersurface of HPn. Let ξ be a unit local normal vector field on M and {I, J,K} a local basis of the quaternionic structure of HPn (cf. [4]). Then U1 = −Iξ, U2 = −Jξ, U3 = −Kξ are unit vector fields tangent to M . We call them structure vectors. Now we put fi(X) = g(X, Ui), for arbitrary X ∈ TM , i = 1, 2, 3, where TM is the tangent bundle of M and g denotes the Riemannian metric induced from the metric G. We denote D and D⊥ the subbundles of TM generated by vectors perpendicular to structure vectors, and structure vectors, respectively. There are many theorems from the point of view of the second fundamental tensor A of M (cf. [1], [8] and [9]). It is known that if M satisfies g(AD,D⊥) = 0 then there is a local basis of quaternionic structure such that structure vectors are principal vectors. Berndt classified the real hypersurfaces which satisfy this condition (cf. [1]). On the other hand we know some results on real hypersurfaces of HPn in terms of the Ricci tensor S of M (cf. [3] and [8]). If the Ricci tensor satisfies that SX = aX + b ∑3 i=1 fi(X)Ui for some smooth functions a and b on M , then M is called a pseudo-Einstein real hypersurface of HPn. This notion comes from the problem for the real hypersurfaces in complex projective space CPn. Kon studied it under the assumption that they have constant coefficients (cf. [5]) and Cecil and Ryan gave a complete classification (cf [2]). In [8] Martinez and Perez studied pseudoEinstein real hypersurfaces of HPn, n = 3, under the condition that a and b are constant. Using Berndt’s classification we show that we do not need the assumption. The main purpose of this paper is to provide a characterization of pseudo-Einstein real hypersurface in HPn by using an estimate of the length of the Ricci tensor S, which is a quaternionic version of a result of Kimura and Maeda (cf. [5]).

1 citations

Book ChapterDOI
05 Aug 2014
TL;DR: MathLibre is a project to archive open source mathematical software and documents and offer them with a Live Linux, and anyone can build modified and localized version of MathLibre, very easily.
Abstract: MathLibre is a project to archive open source mathematical software and documents and offer them with a Live Linux. Anyone can build modified and localized version of MathLibre, very easily.

Cited by
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Journal ArticleDOI
TL;DR: In this paper, the notion of *-Ricci soliton is introduced and real hypersurfaces in non-flat complex space forms admitting a *-ricci s soliton with potential vector field being the structure vector field.

53 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that if a complete Sasakian metric is an almost gradient ∗-Ricci soliton, then it is either positive or null-Sakian.
Abstract: We prove that if a Sasakian metric is a ∗-Ricci Soliton, then it is either positive Sasakian, or null-Sasakian. Next, we prove that if a complete Sasakian metric is an almost gradient ∗-Ricci Solit...

37 citations

Journal ArticleDOI
TL;DR: In this paper, the authors classify real hypersurfaces of complex projective space C P m, m ⩾ 3, with D -recurrent structure Jacobi operator and apply this result to prove the non-existence of such hypersurface with recurrent structure JacobI operator.
Abstract: We classify real hypersurfaces of complex projective space C P m , m ⩾ 3 , with D -recurrent structure Jacobi operator and apply this result to prove the non-existence of such hypersurfaces with recurrent structure Jacobi operator.

32 citations

Journal ArticleDOI
TL;DR: In this paper, the geometry of homogeneous hypersurfaces and their focal sets in complex hyperbolic spaces is studied and a characterization of the focal set in terms of its second fundamental form is provided.
Abstract: We study the geometry of homogeneous hypersurfaces and their focal sets in complex hyperbolic spaces. In particular, we provide a characterization of the focal set in terms of its second fundamental form and determine the principal curvatures of the homogeneous hypersurfaces together with their multiplicities.

29 citations

Journal ArticleDOI
TL;DR: In this paper, the authors considered the case of *-Ricci soliton in the framework of a Kenmotsu manifold and proved that soliton constant λ is zero.
Abstract: Abstract In this paper, we consider *-Ricci soliton in the frame-work of Kenmotsu manifolds. First, we prove that if (M, g) is a Kenmotsu manifold and g is a *-Ricci soliton, then soliton constant λ is zero. For 3-dimensional case, if M admits a *-Ricci soliton, then we show that M is of constant sectional curvature –1. Next, we show that if M admits a *-Ricci soliton whose potential vector field is collinear with the characteristic vector field ξ, then M is Einstein and soliton vector field is equal to ξ. Finally, we prove that if g is a gradient almost *-Ricci soliton, then either M is Einstein or the potential vector field is collinear with the characteristic vector field on an open set of M. We verify our result by constructing examples for both *-Ricci soliton and gradient almost *-Ricci soliton.

29 citations