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Periodica Mathematica Hungarica

, Volume 73, Issue 1, pp 83–92 | Cite as

CR-hypersurfaces of a conformal Kenmotsu manifold satisfying certain shape operator conditions

  • R. Abdi
  • E. Abedi
Article

Abstract

In this paper, conformal Kenmotsu manifolds are introduced. We consider CR-hypersurfaces of a conformal Kenmotsu manifold whose shape operator is parallel, scalar, recurrent or Lie \( \xi \)-parallel. It is proved that if the Lee vector field of a conformal Kenmotsu manifold is tangent and normal to these type of CR-hypersurfaces then the CR-hypersurfaces are totally geodesic and totally umbilic, respectively. An example of a three-dimensional conformal Kenmotsu manifold is constructed for illustration that is not Kenmotsu.

Keywords

Kenmotsu manifold Conformal Kenmotsu manifold 

Mathematics Subject Classification

53C25 53C40 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2016

Authors and Affiliations

  1. 1.Department of MathematicsAzarbaijan shahid Madani UniversityTabrizIran

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