Commun. Korean Math. Soc. 2019; 34(4): 1289-1301
Online first article August 27, 2019 Printed October 31, 2019
https://doi.org/10.4134/CKMS.c180389
Copyright © The Korean Mathematical Society.
Uday Chand De, Gopal Ghosh
University of Calcutta; University of Calcutta
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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