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;

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 is semiparallel if and only if it is totally umbilical with unit mean curvature, if dimM = 3 and is a Calabi-Yau manifold, then 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 -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

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