Characterization of Almost Yamabe Solitons and Gradient Almost Yamabe Solitons with Conformal Vector Fields

In this paper, some sufficient conditions of almost Yamabe solitons are established, such that the solitons are Yamabe metrics, by which we mean metrics of constant scalar curvature. This is achieved by imposing fewer topological constraints. The properties of the conformal vector fields are exploited for the purpose of establishing various necessary criteria on the soliton vector fields of gradient almost Yamabe solitons so as to obtain Yamabe metrics.

[1]  Sharief Deshmukh,et al.  Yamabe and Quasi-Yamabe Solitons on Euclidean Submanifolds , 2017, Mediterranean Journal of Mathematics.

[2]  Mina Teicher,et al.  Homeomorphic Arrangements of Smooth Manifolds , 2021, Symmetry.

[3]  Li Ma,et al.  Properties of complete non-compact Yamabe solitons , 2011 .

[4]  Sharief Deshmukh,et al.  A Note on Ricci Solitons , 2020, Symmetry.

[5]  S. Maeta,et al.  Classification of almost Yamabe solitons in Euclidean spaces , 2017, Journal of Geometry and Physics.

[6]  Sharief Deshmukh,et al.  A Note on Solitons with Generalized Geodesic Vector Field , 2021, Symmetry.

[7]  Bennett Chow,et al.  The yamabe flow on locally conformally flat manifolds with positive ricci curvature , 1992 .

[8]  Richard S. Hamilton,et al.  The Ricci flow on surfaces , 1986 .

[9]  E. Barbosa,et al.  On conformal solutions of the Yamabe flow , 2013 .

[10]  Sharief Deshmukh,et al.  Some Results on Ricci Almost Solitons , 2021, Symmetry.

[11]  F. Al-Solamy,et al.  A note on conformal vector fields on a Riemannian manifold , 2014 .

[12]  Simon Brendle,et al.  Convergence of the Yamabe flow for arbitrary initial energy , 2005 .

[13]  The theory of infinitesimal harmonic transformations and its applications to the global geometry of Riemann solitons , 2019 .

[14]  Hidehiko Yamabe.  On a deformation of Riemannian structures on compact manifolds , 1960 .

[15]  Simon Brendle,et al.  Convergence of the Yamabe flow in dimension 6 and higher , 2007 .

[16]  W. Tokura,et al.  Immersion of gradient almost Yamabe solitons into warped product manifolds , 2020, 2010.03995.

[17]  N. Šešum,et al.  The classification of locally conformally flat Yamabe solitons , 2011, 1104.2242.

[18]  Sharief Deshmukh,et al.  A note on $$\varphi $$φ-analytic conformal vector fields , 2019 .