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Some type of semisymmetry on two classes of almost Kenmotsu manifolds

Dibakar Dey, Pradip Majhi (2021)

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 2 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 2 n + 1 ( - 1 ) are equivalent. Further, it is proved that a ( k , μ ) ' -almost Kenmotsu manifold satisfying...

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