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October 2010 Geometric meaning of Sasakian space forms from the viewpoint of submanifold theory
Toshiaki Adachi, Masumi Kameda, Sadahiro Maeda
Kodai Math. J. 33(3): 383-397 (October 2010). DOI: 10.2996/kmj/1288962549

Abstract

We show that M2n-1 is a real hypersurface all of whose geodesics orthogonal to the characteristic vector ξ are mapped to circles of the same curvature 1 in an n-dimensional nonflat complex space form $\widetilde{M}_n$(c) (= CPn(c) or CHn(c)) if and only if M is a Sasakian manifold with respect to the almost contact metric structure from the ambient space $\widetilde{M}_n$(c). Moreover, this Sasakian manifold M is a Sasakian space form of constant φ-sectional curvature c + 1 for each c (≠0).

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Toshiaki Adachi. Masumi Kameda. Sadahiro Maeda. "Geometric meaning of Sasakian space forms from the viewpoint of submanifold theory." Kodai Math. J. 33 (3) 383 - 397, October 2010. https://doi.org/10.2996/kmj/1288962549

Information

Published: October 2010
First available in Project Euclid: 5 November 2010

zbMATH: 1213.53065
MathSciNet: MR2754328
Digital Object Identifier: 10.2996/kmj/1288962549

Rights: Copyright © 2010 Tokyo Institute of Technology, Department of Mathematics

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Vol.33 • No. 3 • October 2010
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