Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Some type of semisymmetry on two classes of almost Kenmotsu manifolds

Some type of semisymmetry on two classes of almost Kenmotsu manifolds AbstractThe 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 ℍ2n+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 ℍ2n+1(−1) are equivalent. Further, it is proved that a (k, µ)′-almost Kenmotsu manifold satisfying Q · R = 0 is locally isometric to ℍn+1(−4) × ℝn 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 ℍn+1(−4) × ℝn. Finally, an illustrative example is presented. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications in Mathematics de Gruyter

Some type of semisymmetry on two classes of almost Kenmotsu manifolds

Communications in Mathematics , Volume 29 (3): 15 – Dec 1, 2021

Loading next page...
 
/lp/de-gruyter/some-type-of-semisymmetry-on-two-classes-of-almost-kenmotsu-manifolds-kFnZK5kzQx
Publisher
de Gruyter
Copyright
© 2021 Dibakar Dey et al., published by Sciendo
eISSN
2336-1298
DOI
10.2478/cm-2021-0029
Publisher site
See Article on Publisher Site

Abstract

AbstractThe 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 ℍ2n+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 ℍ2n+1(−1) are equivalent. Further, it is proved that a (k, µ)′-almost Kenmotsu manifold satisfying Q · R = 0 is locally isometric to ℍn+1(−4) × ℝn 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 ℍn+1(−4) × ℝn. Finally, an illustrative example is presented.

Journal

Communications in Mathematicsde Gruyter

Published: Dec 1, 2021

Keywords: Almost Kenmotsu manifolds; Semisymmetry; Pseudosymmetry; Hyperbolic space; 53D15; 53C25

There are no references for this article.