In this paper, we characterized a new class of almost contact metric manifolds and established the equivalent conditions of the characterization identity in term of Kirichenko’s tensors We demonstrated that the Kenmotsu manifold provides the mentioned class; ie, the new class can be decomposed into a direct sum of the Kenmotsu and other classes We proved that the manifold of dimension 3 coincided with the Kenmotsu manifold and provided an example of the new manifold of dimension 5, which is not the Kenmotsu manifold Moreover, we established the Cartan’s structure equations, the components of Riemannian curvature tensor and the Ricci tensor of the class under consideration Further, the conditions required for this to be an Einstein manifold have been determined

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A Study of New Class of Almost Contact Metric Manifolds of Kenmotsu Type

On the ricci tensor of submanifolds in conformal kenmotsu manifolds

The object of the present paper is to study submanifolds of a conformal Kenmotsu manifold of which the second fundamental form is recurrent, 2-recurrent or generalized 2-recurrent. Finally, we present an example to verify our results.

External Geometry of Submanifolds in Conformal Kenmotsu Manifolds

In this paper, we study CR-hypersurfaces of a conformal Kenmotsu manifold with a ξ-parallel or Lie ξ-parallel normal Jacobi operator. 2000 Mathematics Subject Classification: 53C25, 53C40.

CR -hypersurfaces of conformal Kenmotsu manifolds with ξ-parallel normal Jacobi operator

We study the CR-hypersurfaces of a conformal Kenmotsu space form with a ξ-parallel normal Jacobi operator. We also present an illustrative example of a three-dimensional conformal Kenmotsu manifold that is not Kenmotsu.

On the Normal Jacobi Operator of CR -Hypersurfaces in Conformal Kenmotsu Space Forms

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.

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

Ovadia and Rodriguez-Hertz (Neutralized local entropy, arXiv:2302.10874) defined the neutralized Bowen open ball for an autonomous dynamical system on a compact metric space. Replacing the usual Bowen open ball with neutralized Bowen open ball, we introduce the notions of neutralized Bowen topological entropy of subsets, neutralized weighted Bowen topological entropy of subsets, lower neutralized Brin-Katok's local entropy of Borel probability measures, and neutralized Katok's entropy of Borel probability measures for a non-autonomous dynamical system on a compact metric space. Then, we establish variational principles for neutralized Bowen topological entropy and neutralized weighted Bowen topological entropy of non-empty compact subsets in terms of lower neutralized Brin-Katok's local entropy and neutralized Katok's entropy. In particular, this extends the main result of (YANG, R., CHEN, E., ZHOU, X.: Variational principle for neutralized Bowen topological entropy, arXiv:2303.01738v1) for autonomous dynamical systems.

Roghayeh Abdi

Papers

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

On the ricci tensor of submanifolds in conformal kenmotsu manifolds

External Geometry of Submanifolds in Conformal Kenmotsu Manifolds

On the Normal Jacobi Operator of CR -Hypersurfaces in Conformal Kenmotsu Space Forms

Variational principle for neutralized Bowen topological entropy on subsets of non-autonomous dynamical systems