On semiparallel and weyl-semiparallel hypersurfaces of kaehler manifolds


Özgür C., MURATHAN C. , ARSLAN K.

Kyungpook Mathematical Journal, vol.49, no.1, pp.133-141, 2009 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 1
  • Publication Date: 2009
  • Doi Number: 10.5666/kmj.2009.49.1.133
  • Title of Journal : Kyungpook Mathematical Journal
  • Page Numbers: pp.133-141

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.