A classification of $(k,\mu)'$-almost Kenmotsu manifolds admitting Cotton tensor

Dibakar Dey,Pradip Majhi̇

doi:10.31801/cfsuasmas.699780

Abstract

The object of the present paper is to classify $(k,\mu)'$-almost Kenmotsu manifolds admitting Cotton tensors. We characterize $(k,\mu)'$-almost Kenmotsu manifolds with vanishing and parallel Cotton tensors. Beside this, $(k,\mu)'$-almost Kenmotsu manifolds satisfying Cotton semisymmetry and $Q(g,C) = 0$ are studied. Further, Cotton pseudo-symmetric $(k,\mu)'$-almost Kenmotsu manifolds are classified.

Highlights

IntroductionOn a (2n + 1)-dimensional Riemannian manifold (M 2n+1; g), the (0; 3)-Cotton tensor C is de...ned by [9]
On a (2n + 1)-dimensional Riemannian manifold (M 2n+1; g), the (0; 3)-Cotton tensor C is de...ned by [9]C(X; Y )Z =(Y; Z)(X; Z)1 4n ((Xr)g(Y; Z) (Y r)g(X; Z)); (1.1)where S and r denotes Ricci tensor and scalar curvature of M respectively
A (k; )0-almost Kenmotsu manifold M 2n+1 with h0 6= 0 is Cotton parallel if and only if M 2n+1 is locally isometric to the Riemannian product of an (n + 1)-dimensional manifold of constant sectional curvature 4 and a ‡at ndimensional manifold

Summary

Introduction

On a (2n + 1)-dimensional Riemannian manifold (M 2n+1; g), the (0; 3)-Cotton tensor C is de...ned by [9]. As it is well known that a Riemannian manifold (M n; g) is locally conformally ‡at if and only if (1) for n 4 the Weyl tensor vanishes, (2) n = 3 the Cotton tensor vanishes. In [1], pseudo-symmetric contact metric manifolds were studied by Arslan et al . Pseudo-symmetric Riemannian spaces were studied by Özen and Altay [13]. -conformally ‡at K-contact manifolds have been studied by Zhen et al [21]. A semi-Riemannian manifold M is said to be of Codazzi type Ricci tensor if, (rX S)(Y; Z) = (rY S)(X; Z) for any vector ...elds X; Y and Z holds on M.

Preliminaries

Conclusion