Geometry of $(\kappa,\mu)'$-almost Kenmotsu manifolds with divergence free Cotton tensor and vanishing Bach tensor

B. M. Sowmyashree; H. Aruna Kumara; P. Siva Kota Reddy

doi:10.5269/bspm.76100

B. M. Sowmyashree JSS Science and Technology University
H. Aruna Kumara BMS Institute of Technology and Management, Bangalore, India
P. Siva Kota Reddy JSS Science and Technology University, Mysuru

Abstract

In this paper, we prove that a non-Kenmotsu $(\kappa,\mu)'$-almost Kenmotsu manifold of dimension $(2n+1)$ has divergence free Cotton tensor if and only if it is locally isometric to the Riemannian product $\mathbb{H}^{n+1}(-4)\times\mathbb{R}^n$. Finally, we show that a Bach flat non-Kenmotsu $(\kappa,\mu)'$-almost Kenmotsu manifold is 3-dimensional and is locally isometric to the Riemannian product $\mathbb{H}^2(-4)\times\mathbb{R}$.

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Author Biographies

H. Aruna Kumara, BMS Institute of Technology and Management, Bangalore, India

Assistant Professor, Department of Mathematics

P. Siva Kota Reddy, JSS Science and Technology University, Mysuru

Professor and Head, Department of Mathematics

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