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http://dx.doi.org/10.4134/CKMS.c180389

SOME RESULTS ON ALMOST KENMOTSU MANIFOLDS WITH GENERALIZED (k, µ)'-NULLITY DISTRIBUTION  

De, Uday Chand (Department of Pure Mathematics University of Calcutta)
Ghosh, Gopal (Department of Pure Mathematics University of Calcutta)
Publication Information
Communications of the Korean Mathematical Society / v.34, no.4, 2019 , pp. 1289-1301 More about this Journal
Abstract
In the present paper, we prove that if there exists a second order parallel tensor on an almost Kenmotsu manifold with generalized $(k,{\mu})^{\prime}$-nullity distribution and $h^{\prime}{\neq}0$, 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 $(k,{\mu})^{\prime}$-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;
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Times Cited By KSCI : 4  (Citation Analysis)
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