Hypersurfaces of a Sasakian space form with recurrent shape operator

Document Type: Research Paper

Authors

Department of‎ ‎Mathematics‎, ‎Azarbaijan Shahid Madani University‎, ‎P.O‎. ‎Box 53751 71379‎, ‎Tabriz‎, ‎Iran

Abstract

Let $(M^{2n},g)$ be a real hypersurface with recurrent shape
operator and tangent to the structure vector field $xi$ of the Sasakian space form
$widetilde{M}(c)$. We show that if the shape operator $A$ of $M$ is
recurrent then it is parallel. Moreover, we show that $M$
is locally a product of two constant $phi-$sectional curvature
spaces.

Keywords

Main Subjects



Volume 41, Issue 5
September and October 2015
Pages 1287-1297
  • Receive Date: 18 September 2012
  • Revise Date: 03 August 2014
  • Accept Date: 08 August 2014