Second Order Parallel Tensor on Almost Kenmotsu Manifolds

Venkatesha Venkatesha; Devaraja Mallesha Naik; Aysel-Turgut Vanli

doi:10.5666/KMJ.2021.61.1.191

Article

Kyungpook Mathematical Journal 2021; 61(1): 191-203

Published online March 31, 2021

Second Order Parallel Tensor on Almost Kenmotsu Manifolds

Venkatesha Venkatesha^*, Devaraja Mallesha Naik, Aysel-Turgut Vanli

Department of Mathematics, Kuvempu University, Shivamogga 577-451, India
e-mail : vensmath@gmail.com

Department of Mathematics, Kuvempu University, Shivamogga 577-451, India Department of Mathematics, CHRIST (Deemed to be University), Bengaluru 560029, Karnataka, India
e-mail : devaraja.mallesha@christuniversity.in

Department of Mathematics, Gazi University, Ankara, Turkey
e-mail : avanli@gazi.edu.tr

Received: November 14, 2019; Revised: July 18, 2020; Accepted: July 21, 2020

Abstract

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Abstract

Let M be an almost Kenmotsu manifold of dimension 2n+1 having non-vanishing ξ-sectional curvature such that trl>−2n−2. We prove that any second order parallel tensor on M is a constant multiple of the associated metric tensor and obtained some consequences of this. Vector fields keeping curvature tensor invariant are characterized on M.

Keywords: almost Kenmotsu manifold, second order parallel tensor, nullity distribution, homothetic vector field.