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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 $H^{3}(-1)$.
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참고문헌 (37)
참고문헌 신청
Kadri Arslan / 2005 / Contact CR-Warped Product Submanifolds in Kenmotsu Space Forms / 대한수학회지 42(5):1101~1110
A. Ba¸sari / 2008 / On generalized φ-recurrent Kenmotsu manifolds / Fen Derg 3(1):91~97
A. L. Besse / 2008 / Classics in Mathematics / Springer-Verlag
D. E. Blair / 1976 / Contact manifolds in Riemannian geometry / Springer-Verlag
W. M. Boothby / 1958 / On Contact Manifolds / The Annals of Mathematics 68(3):721
A. Ba¸sari / 2008 / On generalized φ-recurrent Kenmotsu manifolds / Fen Derg 3(1):91~97
A. L. Besse / 2008 / Classics in Mathematics / Springer-Verlag
D. E. Blair / 1976 / Contact manifolds in Riemannian geometry / Springer-Verlag
W. M. Boothby / 1958 / On Contact Manifolds / The Annals of Mathematics 68(3):721
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