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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