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Kenmotsu manifolds satisfying the Fischer-Marsden equation

Uday Chand De|서영진|Sudhakar Kr Chaubey
대한수학회 (The Korean Mathematical Society)|2021.05|대한수학회지 (Journal of the KMS)|제58권 제3호|pp. 597-607|DOI 10.4134/JKMS.j190602

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키워드

Einstein manifoldFischer-Marsden equationKenmotsu manifoldsspace-form
주제분류수학

초록

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 $H^{3}(-1)$.

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 $\mathfrak{L}^{*}_{g}(\lambda)=0$ 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 $H^{3}(-1)$.

참고문헌 (37)

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