Some results on almost Kenmotsu manifolds with generalized $(k,\mu)'$-nullity distribution
Commun. Korean Math. Soc. 2019 Vol. 34, No. 4, 1289-1301
Published online October 31, 2019
Uday Chand De, Gopal Ghosh
University of Calcutta; University of Calcutta
Abstract : In the present paper, we prove that if there exists a second order parallel tensor on an almost Kenmotsu manifold with generalized $(k,\mu)'$-nullity distribution and $h' \neq 0$, then either the manifold is isometric to $H^{n+1}(-4)\times\mathbb{R}^{n}$, or, the second order parallel tensor is a constant multiple of the associated metric tensor of $M^{2n+1}$ under certain restriction on $k, \mu$. Besides this, we study Ricci soliton on an almost Kenmotsu manifold with generalized $(k,\mu)'$-nullity distribution. Finally, we characterize such a manifold admitting generalized Ricci soliton.
Keywords : almost Kenmotsu manifold, generalized nullity distribution, second order parallel tensor, Ricci soliton, generalized Ricci soliton
MSC numbers : Primary 53C15, 53C25
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