Communications in Mathematics |

The object of the present paper is to study some types of semisymmetry conditions on two classes of almost Kenmotsu manifolds. It is shown that a (k, µ)-almost Kenmotsu manifold satisfying the curvature condition Q · R = 0 is locally isometric to the hyperbolic space ℍ2 n +1(−1). Also in (k, µ)-almost Kenmotsu manifolds the following conditions: (1) local symmetry (∇R = 0), (2) semisymmetry (R·R = 0), (3) Q(S, R) = 0, (4) R·R = Q(S, R), (5) locally isometric to the hyperbolic space ℍ2 n +1(−1) are equivalent. Further, it is proved that a (k, µ) ′ -almost Kenmotsu manifold satisfying Q · R = 0 is locally isometric to ℍ n +1(−4) × ℝ n and a (k, µ) ′- -almost Kenmotsu manifold satisfying any one of the curvature conditions Q(S, R) = 0 or R · R = Q(S, R) is either an Einstein manifold or locally isometric to ℍ n +1(−4) × ℝ n . Finally, an illustrative example is presented.

Source: HAL:hal-03665029v1

Volume: Volume 29 (2021), Issue 3

Published on: December 23, 2021

Imported on: May 11, 2022

Keywords: General Mathematics,[MATH]Mathematics [math]

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