Kodai Mathematical Journal

Geometric meaning of Sasakian space forms from the viewpoint of submanifold theory

Toshiaki Adachi, Masumi Kameda, and Sadahiro Maeda

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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).

Article information

Source
Kodai Math. J., Volume 33, Number 3 (2010), 383-397.

Dates
First available in Project Euclid: 5 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1288962549

Digital Object Identifier
doi:10.2996/kmj/1288962549

Mathematical Reviews number (MathSciNet)
MR2754328

Zentralblatt MATH identifier
1213.53065

Citation

Adachi, Toshiaki; Kameda, Masumi; Maeda, Sadahiro. Geometric meaning of Sasakian space forms from the viewpoint of submanifold theory. Kodai Math. J. 33 (2010), no. 3, 383--397. doi:10.2996/kmj/1288962549. https://projecteuclid.org/euclid.kmj/1288962549


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