On Semiparallel and Weyl-semiparallel Hypersurfaces of Kaehler Manifolds

• Journal title : Kyungpook mathematical journal
• Volume 49, Issue 1,  2009, pp.133-141
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2009.49.1.133
Title & Authors
On Semiparallel and Weyl-semiparallel Hypersurfaces of Kaehler Manifolds
Ozgur, Cihan; Murathan, Cengizhan; Arslan, Kadri;

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 $\small{\widetilde{M}^{2n+2}}$ is semiparallel if and only if it is totally umbilical with unit mean curvature, if dimM = 3 and $\small{\widetilde{M}^4}$ is a Calabi-Yau manifold, then $\small{\widetilde{M}}$ 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 $\small{{\eta}}$-Einstein manifold or semiparallel. We also investigate the extended classes of semiparallel and Weyl semiparallel Sasakian hypersurfaces of Kaehler manifolds.
Keywords
Sasakian manifold;Kaehler manifold;Calabi-Yau manifold;semiparallel submanifold;Weyl-semiparallel submanifold;pseudoparallel submanifold;
Language
English
Cited by
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