Hokkaido Mathematical Journal

Real hypersurfaces which are contact in a nonflat complex space form

Toshiaki ADACHI, Masumi KAMEDA, and Sadahiro MAEDA

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Abstract

In an $n$ $(\geqq2)$-dimensional nonflat complex space form $\widetilde{M}_n(c)(=\mathbb{C}P^n(c)$ or $\mathbb{C}H^n(c)$), we classify real hypersurfaces $M^{2n-1}$ which are contact with respect to the almost contact metric structure $(\phi,\xi,\eta,g)$ induced from the K\"ahler structure $J$ and the standard metric $g$ of the ambient space $\widetilde{M}_n(c)$. Our theorems show that this contact manifold $M^{2n-1}$ is congruent to a homogeneous real hypersurface of $\widetilde{M}_n(c)$.

Article information

Source
Hokkaido Math. J., Volume 40, Number 2 (2011), 205-217.

Dates
First available in Project Euclid: 7 July 2011

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1310042828

Digital Object Identifier
doi:10.14492/hokmj/1310042828

Mathematical Reviews number (MathSciNet)
MR2840106

Zentralblatt MATH identifier
1232.53045

Subjects
Primary: 53C40: Global submanifolds [See also 53B25]
Secondary: 53C22: Geodesics [See also 58E10] 53D10: Contact manifolds, general

Keywords
nonflat complex space forms real hypersurfaces totally $\eta$-umbilic hypersurfaces standard real hypersurfaces homogeneous real hypersurfaces of type (B) almost contact metric structure contact manifolds Sasakian manifolds Sasakian space forms

Citation

ADACHI, Toshiaki; KAMEDA, Masumi; MAEDA, Sadahiro. Real hypersurfaces which are contact in a nonflat complex space form. Hokkaido Math. J. 40 (2011), no. 2, 205--217. doi:10.14492/hokmj/1310042828. https://projecteuclid.org/euclid.hokmj/1310042828


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