Showing papers by "Young Jin Suh published in 2003"
TL;DR: In this article, it was shown that there do not exist any real hypersurfaces in a complex two-dimensional Grassmannians G2(n+2) with parallel shape operator.
Abstract: In this paper we show that there do not exist any real hypersurfaces in a complex two dimensional Grassmannians G2(ℂn+2) with parallel shape operator.
56 citations
TL;DR: In this article, a non-existence property of real hypersurfaces in complex two-plane Grassmannians G2(ℂm+2) with a shape operator A commuting with the structure tensors was shown.
Abstract: In this paper we give a non-existence property of real hypersurfaces in complex two-plane Grassmannians G2(ℂm+2) which have a shape operator A commuting with the structure tensors {φ1, φ2, φ3} From this view point we give a characterisation of real hypersurfaces of type B in G2(ℂm+2)
30 citations
TL;DR: In this paper, the authors introduce new notions of Ricci-like tensors and many kind of curvature-like (conformal) tensors such as concir-cular, projective, or conformal curvature tensors defined on semi-Riemannian manifolds.
Abstract: In this paper we introduce new notions of Ricci-like tensor and many kind of curvature-like tensors such that concir- cular, projective, or conformal curvature-like tensors defined on semi-Riemannian manifolds. Moreover, we give some geometric conditions which are equivalent to the Codazzi tensor, the Weyl tensor, or the second Bianchi identity concerned with such kind of curvature-like tensors respectively and also give a generalization of Weyl's Theorem given in (18) and (19).
27 citations
TL;DR: In this paper, the authors define the Jacobi operator of a Riemannian manifold with respect to any tangent vector and show that any real, complex and quaternionic space forms satisfy that any two Jacobi operators commute.
Abstract: From the classical differential equation of Jacobi fields, one naturally defines the Jacobi operator of a Riemannian manifold with respect to any tangent vector. A straightforward computation shows that any real, complex and quaternionic space forms satisfy that any two Jacobi operators commute. In this way, we classify the real hypersurfaces in quaternionic projective spaces all of whose tangent Jacobi operators commute. 2000 Mathematics Subject Classification. 53C15, 53B25.
5 citations
TL;DR: In this paper, the authors give a complete classification of real hypersurfces M in complex space forms Mn(c), c≠0 in terms of an η-parallel curvature tensor and a certain commutative condition defined on the distribution T0={X∈TxM| X⊥ξ} of M in Mn (c).
Abstract: The purpose of this paper is to give a complete classification of real hypersurfces M in complex space forms Mn(c), c≠0 in terms of an η-parallel curvature tensor and a certain commutative condition defined on the distribution T0={X∈TxM| X⊥ξ} of M in Mn(c).
4 citations
01 Jan 2003
TL;DR: In this article, the authors give a characterization of an irre-ducible connection with harmonic curvature over a connected Kaeh- ler manifold to be self-dual.
Abstract: In this paper we give a characterization of an irre- ducible connection with harmonic curvature over a connected Kaeh- ler manifold to be self-dual. Also we introduce new notions of ci-self-dual or Kaehler Yang-Mills connections on compact Kaehler manifolds and investigate some fundamental properties of this kind of new connections. Moreover, on a compact odd dimensional Rie- mannian manifold we give a property of generalized monopole.
TL;DR: In this article, the authors give a characterization of irreducible connection with harmonic curvature over a connected Kaehler manifold to be self-dual, and introduce new notions of or kaehler Yang-Mills connections.
Abstract: In this paper we give a characterization of an irreducible connection with harmonic curvature over a connected Kaehler manifold to be self-dual. Also we introduce new notions of or Kaehler Yang-Mills connections on compact Kaehler manifolds and investigate some fundamental properties of this kind of new connections. Moreover, on a compact odd dimensional Riemannian manifold we give a property of generalized monopole.