*-Ricci soliton on (κ, μ)′-almost Kenmotsu manifolds
TLDR
In this article, it was shown that if the metric g of M is a *-Ricci soliton, then either M is locally isometric to the product ℍn+1(−4)×ℝn or the potential vector field is strict infinitesimal contact transformation.Abstract:
Abstract Let (M, g) be a non-Kenmotsu (κ, μ)′-almost Kenmotsu manifold of dimension 2n + 1. In this paper, we prove that if the metric g of M is a *-Ricci soliton, then either M is locally isometric to the product ℍn+1(−4)×ℝn or the potential vector field is strict infinitesimal contact transformation. Moreover, two concrete examples of (κ, μ)′-almost Kenmotsu 3-manifolds admitting a Killing vector field and strict infinitesimal contact transformation are given.read more
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∗ -Ricci Tensor on α -Cosymplectic Manifolds
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Critical point equation on a class of almost Kenmotsu manifolds
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$\ast$-Conformal Ricci soliton on a class of almost Kenmotsu manifolds
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Ricci Soliton and Certain Related Metrics on a Three-Dimensional Trans-Sasakian Manifold
TL;DR: In this paper , a Ricci soliton and *-conformal Ricci s soliton are examined in the framework of trans-Sasakian three-manifolds.
References
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Three-manifolds with positive Ricci curvature
Book
Riemannian Geometry of Contact and Symplectic Manifolds
TL;DR: In this article, the authors describe a complex geometry model of Symplectic Manifolds with principal S1-bundles and Tangent Sphere Bundles, as well as a negative Xi-sectional Curvature.
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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