Ruled real hypersurfaces of complex space forms
01 Mar 2010-Kodai Mathematical Journal (Department of Mathematics, Tokyo Institute of Technology)-Vol. 33, Iss: 1, pp 123-134
About: This article is published in Kodai Mathematical Journal.The article was published on 2010-03-01 and is currently open access. It has received 15 citations till now. The article focuses on the topics: Ricci decomposition & Weyl tensor.
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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
TL;DR: In this paper, the classification result of real hypersurfaces with constant principal curvatures in nonflat complex space forms and whose Hopf vector field has nontrivial projection onto two eigenspaces of the shape operator was presented.
Abstract: We present the motivation and current state of the classification problem of real hypersurfaces with constant principal curvatures in complex space forms. In particular, we explain the classification result of real hypersurfaces with constant principal curvatures in nonflat complex space forms and whose Hopf vector field has nontrivial projection onto two eigenspaces of the shape operator. This constitutes the following natural step after Kimura and Berndtʼs classifications of Hopf real hypersurfaces with constant principal curvatures in complex space forms.
19 citations
TL;DR: In this paper, the authors investigated φ-Einstein contact Riemannian manifolds and applied it to Mathematics Subject Classification (2010) and found that φ = 0.
Abstract: φ-Einstein contact Riemannian manifolds are investigated. Mathematics Subject Classification (2010). Primary 58E20.
8 citations
8 citations
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4 citations
TL;DR: In this article, a classification of real hypersurfaces in a non-flat complex space form, whose almost contact structure operator, induced from the complex structure of the complex space, commutes with the Ricci operator and at the same time commutates with the structural Jacobi operator, is given.
Abstract: We give a classification of real hypersurfaces in a non-flat complex space form, whose almost contact structure operator, induced from the complex structure of the complex space form, commutes with the Ricci operator and at the same time commutes with the structural Jacobi operator. In particular, we classify real hypersurfaces in 2-dimensional complex projective and hyperbolic spaces satisfying the first commutativity condition.
3 citations