Journal of the
Korean Mathematical Society JKMS

The present paper deals with the study of Fischer-Marsden conjecture on a Kenmotsu manifold. It is proved that if a Kenmotsu metric satisfies $\mathfrak{L}^{*}_{g}(\lambda)=0$ on a $(2n+1)$-dimensional Kenmotsu manifold $M^{2n+1}$, then either $\xi \lambda=- \lambda$ or $M^{2n+1}$ is Einstein. If $n=1$, $M^3$ is locally isometric to the hyperbolic space $H^{3}(-1)$.

Keywords: Fischer-Marsden equation, Kenmotsu manifolds, Einstein manifold, space-form

MSC numbers: 53C25, 53C15

Supported by: The Third author is supported by Grant Project No. NRF-2018-R1D1A1B-05040381 from National Research Foundation of Korea. First author acknowledges authority of Shinas College of Technology for their continuous support and encouragement to carry out this research work.