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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Azarbaijan shahid Madani University, Tabriz, 53751 71379, Iran

    R. Abdi & E. Abedi

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  1. R. Abdi
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  2. E. Abedi
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Correspondence to R. Abdi.

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Abdi, R., Abedi, E. CR-hypersurfaces of a conformal Kenmotsu manifold satisfying certain shape operator conditions. Period Math Hung 73, 83–92 (2016). https://doi.org/10.1007/s10998-016-0131-6

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  • DOI: https://doi.org/10.1007/s10998-016-0131-6

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