Some type of semisymmetry on two classes of almost Kenmotsu manifolds

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 ( )-almost Kenmotsu manifold satisfying the curvature condition · = 0 is locally isometric to the hyperbolic space ℍ 1). Also in ( )-almost Kenmotsu manif...

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Veröffentlicht in:Communications in Mathematics 2021-12, Vol.29 (3), p.457-471
Hauptverfasser: Dey, Dibakar, Majhi, Pradip
Format: Artikel
Sprache:eng
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Zusammenfassung: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 ( )-almost Kenmotsu manifold satisfying the curvature condition · = 0 is locally isometric to the hyperbolic space ℍ 1). Also in ( )-almost Kenmotsu manifolds the following conditions: (1) local symmetry (∇ = 0), (2) semisymmetry ( = 0), (3) ) = 0, (4) = ), (5) locally isometric to the hyperbolic space ℍ (−1) are equivalent. Further, it is proved that a ( -almost Kenmotsu manifold satisfying · = 0 is locally isometric to ℍ 4) ℝ and a ( -almost Kenmotsu manifold satisfying any one of the curvature conditions ) = 0 or · = ) is either an Einstein manifold or locally isometric to ℍ (−4) ℝ . Finally, an illustrative example is presented.
ISSN:2336-1298
1804-1388
2336-1298
DOI:10.2478/cm-2021-0029