Critical point equation on almost Kenmotsu manifolds

  • U. C. De Univ. Calcutta, West Bengal, India
  • K.  Mandal Univ. Calcutta, West Bengal, India
Keywords: Almost Kenmotsu manifold, nullity distribution, critical point equation, Einstein manifold

Abstract

We study the critical point equation $(CPE)$ conjecture on almost Kenmotsu manifolds.
First, we prove that if a three-dimensional $(k,\mu)'$-almost Kenmotsu manifold satisfies the $CPE,$ then the manifold is either locally isometric to the product space $\mathbb H^2(-4)\times\mathbb R$ or the manifold is Kenmotsu manifold. Further, we prove that if the metric of an almost Kenmotsu manifold with conformal Reeb foliation satisfies the $CPE$ conjecture, then the manifold is Einstein.

 

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Published
15.01.2020
How to Cite
De U. C., and Mandal K. “Critical Point Equation on Almost Kenmotsu Manifolds”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 1, Jan. 2020, pp. 61-68, https://umj.imath.kiev.ua/index.php/umj/article/view/2330.
Section
Research articles