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 (CM C) hypersurface of a Bochner-Kaehler manifold is a (k, µ)-contact manifold, and (2) If M is a compact contact metric CM C 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.