Contact Hypersurfaces of a Bochner-Kaehler Manifold

Abstract

We have studied contact metric hypersurfaces of a Bochner-Kaehler manifold and obtained the following two results: (1) a contact metric constant mean curvature (CMC) hypersurface of a Bochner-Kaehler manifold is a (k, μ)-contact manifold, and (2) if M is a compact contact metric CMC hypersurface of a Bochner-Kaehler manifold with a conformal vector field V that is neither tangential nor normal anywhere, then it is totally umbilical and Sasakian, and under certain conditions on V, is isometric to a unit sphere. © 2013 Springer Basel.