∗-Ricci solitons and gradient almost ∗-Ricci solitons on Kenmotsu manifolds
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In this paper, the authors considered the case of *-Ricci soliton in the framework of a Kenmotsu manifold and proved that soliton constant λ is zero.Abstract:
Abstract In this paper, we consider *-Ricci soliton in the frame-work of Kenmotsu manifolds. First, we prove that if (M, g) is a Kenmotsu manifold and g is a *-Ricci soliton, then soliton constant λ is zero. For 3-dimensional case, if M admits a *-Ricci soliton, then we show that M is of constant sectional curvature –1. Next, we show that if M admits a *-Ricci soliton whose potential vector field is collinear with the characteristic vector field ξ, then M is Einstein and soliton vector field is equal to ξ. Finally, we prove that if g is a gradient almost *-Ricci soliton, then either M is Einstein or the potential vector field is collinear with the characteristic vector field on an open set of M. We verify our result by constructing examples for both *-Ricci soliton and gradient almost *-Ricci soliton.read more
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Riemann solitons and almost Riemann solitons on almost Kenmotsu manifolds
TL;DR: In this paper, the authors studied the Riemann soliton and gradient almost-Riemann-soliton on a certain class of almost Kenmotsu manifolds.
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Kenmotsu Metric as Conformal $$\eta $$-Ricci Soliton
TL;DR: In this article , the authors investigated the nature of the conformal Ricci soliton within the framework of Kenmotsu manifolds and established a relation between the potential vector field and the Reeb vector field.
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Kenmotsu metric as conformal $\eta$-Ricci soliton
TL;DR: In this paper, the authors investigated the nature of the conformal Ricci soliton within the framework of Kenmotsu manifolds and established a relation between the potential vector field and the Reeb vector field.
References
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Journal ArticleDOI
A class of almost contact riemannian manifolds
TL;DR: In this article, Tanno has classified connected almost contact Riemannian manifolds whose automorphism groups have themaximum dimension into three classes: (1) homogeneous normal contact manifolds with constant 0-holomorphic sec-tional curvature if the sectional curvature for 2-planes which contain
Journal ArticleDOI
Certain Results on K-Contact and (k, μ)-Contact Manifolds
TL;DR: In this article, Boyer and Galicki showed that a complete K-contact gradient soliton is a Jacobi vector field along the geodesics of the Reeb vector field.
Journal ArticleDOI
Real Hypersurfaces of Complex Space Forms in Terms of Ricci $*$-Tensor
TL;DR: In this article, the authors classified the $*$-Einstein real hypersurfaces in complex space forms such that the structure vector is a principal curvature vector and the principal curvatures of the hypersurface can be computed with the K\"ahler metric.
Journal ArticleDOI
Kenmotsu 3-metric as a Ricci soliton
TL;DR: In this paper, it was shown that if a 3D Kenmotsu metric is a Ricci soliton, then it is of constant curvature −1 and the soliton is expanding.