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).
Citation
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
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