Real hypersurfaces which are contact in a nonflat complex space form

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 $\widetilde{M}_n(c)$.