In this paper, biharmonic Hopf hypersurfaces in the complex Euclidean space C n+1 and in the odd dimensional sphere S 2n+1 are considered. We prove that the biharmonic Hopf hypersurfaces in C n+1 are minimal. Also, we determine that the Weingarten operator A of a biharmonic pseudo-Hopf hypersurface in the unit sphere S 2n+1 has exactly two distinct principal curvatures at each point if the gradient of the mean curvature belongs to D ⊥ , and thus is an open part of the Clifford hypersurface S n1 (1/ √ 2) × S n2 (1/ √ 2), where n 1 + n 2 = 2n.
In this paper, we obtain several interesting results on submanifolds of conformal Kenmotsu manifolds. In addition to this we consider submanifolds of a conformal Kenmotsu manifold of which the Ricci tensor is parallel, Lie ξ-parallel or recurrent. We also present an illustration example of a three-dimensional conformal Kenmotsu manifold that is not Kenmotsu.
In this paper, Conformal Kenmotsu manifolds are introduced which are not Kenmotsu. We consider CR-hypersurfaces of a conformal Kenmotsu space form whose shape operator is parallel, scalar, recurrent or Lie ξ-parallel, it is proved that if the Lee vector field of a conformal Kenmotsu space form is tangent and normal to these type CR-hypersurfaces then the CR-hypersurfaces are totally geodesic and totally umbilic, respectively.
UDC 515.12
We investigate biharmonic Ricci soliton hypersurfaces whose potential field satisfies certain conditions. We obtain a result based on the average scalar curvature of the compact Ricci soliton hypersurface where is a general vector field. Then we prove that there are no proper biharmonic Ricci soliton hypersurfaces in the Euclidean space provided that the potential field is either a principal vector in grad or .
In this paper we classify pseudosymmetric and Ricci-pseudosymmetric (κ, µ)-contact metric manifolds in the sense of Deszcz. Next we characterize Weyl-pseudosymmetric (κ, µ)-contact metric manifolds.
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