KENMOTSU MANIFOLDS SATISFYING THE FISCHER-MARSDEN EQUATION
J. Korean Math. Soc.
Published online March 6, 2020
Sudhakar Kr Chaubey, Uday Chand De, and Young Jin Suh
Shinas College of Technology, University of Calcutta, Kyungpook National University
Abstract : The present paper deals with the study of Fischer-Marsden conjecture on a Kenmotsu manifold. It is proved that if a Kenmotsu metric satisfies $\mathfrak{L}^{*}_{g}(\lambda)=0$ within the framework of a $(2n+1)$-dimensional Kenmotsu manifold $M^{2n+1}$, then either $(\xi \lambda)=- \lambda$ or $M^{2n+1}$ is Einstein and $M^3$ is locally isometric to the hyperbolic space $H^{3}(-1)$.
Keywords : Fischer-Marsden equation, Kenmotsu manifolds, Einstein manifold, space-form
MSC numbers : 53C25, 53C15
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