Real hypersurfaces with an induced almost contact structure
Volume 114 / 2009
Colloquium Mathematicum 114 (2009), 41-51
MSC: 53A15, 53D15.
DOI: 10.4064/cm114-1-5
Abstract
We study real affine hypersurfaces $f\colon M\rightarrow\mathbb C^{n+1}$ with an almost contact structure $(\varphi,\xi,\eta)$ induced by any $J$-tangent transversal vector field. The main purpose of this paper is to show that if $(\varphi,\xi,\eta)$ is metric relative to the second fundamental form then it is Sasakian and moreover $f(M)$ is a piece of a hyperquadric in $\mathbb R^{2n+2}$.
