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Abstract
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In this paper, conformal Kenmotsu manifolds are introduced. We consider CRhypersurfaces
of a conformal Kenmotsu manifold whose shape operator is parallel, scalar,
recurrent or Lie ξ -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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