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Some results on almost Kenmotsu manifolds with generalized $(k,\mu)'$-nullity distribution

Uday Chand De|Gopal Ghosh
대한수학회 (The Korean Mathematical Society)|2019.10|대한수학회논문집 (Communications of the KMS)|제34권 제4호|pp. 1289-1301|DOI 10.4134/CKMS.c180389

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키워드

Ricci solitonalmost Kenmotsu manifoldgeneralized nullity distributionsecond order parallel tensorgeneralized Ricci soliton
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초록

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.

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.

참고문헌 (36)

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관련 논문AI추천

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