Hokkaido Mathematical Journal

ADACHI Toshiaki, KAMEDA Masumi, MAEDA Sadahiro,

Real hypersurfaces which are contact in a nonflat complex space form.

Hokkaido Mathematical Journal, 40 (2011) pp.205-217

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Abstract

In an $n$ $(\ge 2)$-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 $\widetilde{M}_n(c)$.

MSC(Primary)53C40
MSC(Secondary)53C22, 53D10
Uncontrolled Keywordsnonflat 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