On semiparallel and weyl-semiparallel hypersurfaces of kaehler manifolds

Abstract

We study on semiparallel and Weyl semiparallel Sasakian hypersurfaces of Kaehler manifolds. We prove that a (2n + 1)-dimensional Sasakian hypersurface M of a (2n+2)-dimensional Kaehler manifold M2n+2 is semiparallel if and only if it is totally umbilical with unit mean curvature, if dimM = 3 and M4 is a Calabi-Yau manifold, then M is flat at each point of M. We also prove that such a hypersurface M is Weyl-semiparallel if and only if it is either an η-Einstein manifold or semiparallel. We also investigate the extended classes of semiparallel and Weyl semiparallel Sasakian hypersurfaces of Kaehler manifolds.