Some type of semisymmetry on two classes of almost Kenmotsu manifolds

Q3 Mathematics
D. Dey, P. Majhi
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引用次数: 1

Abstract

Abstract 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 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.
两类几乎Kenmotsu流形上的一类半对称性
摘要本文的目的是研究两类几乎Kenmotsu流形上的一些类型的半对称性条件。证明了满足曲率条件Q·R=0的(k,µ)-概Kenmotsu流形与双曲空间是局部等距的ℍ2n+1(−1)。同样在(k,µ)-几乎Kenmotsu流形中,以下条件:(1)局部对称性(ŞR=0),(2)半对称性(R·R=0)、(3)Q(S,R)=0,(4)R·R=Q(S、R),(5)双曲空间的局部等距ℍ2n+1(−1)是等价的。进一步证明了满足Q·R=0的(k,µ)′-几乎Kenmotsu流形与ℍn+1(−4)×ℝn和满足任意一个曲率条件Q(S,R)=0或R·R=Q(S、R)的(k,µ)′-几乎Kenmotsu流形是Einstein流形或局部等距于ℍn+1(−4)×ℝ最后,给出了一个示例。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Communications in Mathematics
Communications in Mathematics Mathematics-Mathematics (all)
CiteScore
1.00
自引率
0.00%
发文量
26
审稿时长
45 weeks
期刊介绍: Communications in Mathematics publishes research and survey papers in all areas of pure and applied mathematics. To be acceptable for publication, the paper must be significant, original and correct. High quality review papers of interest to a wide range of scientists in mathematics and its applications are equally welcome.
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