Rigidity of almost Ricci solitons on compact Riemannian manifolds
Considering an almost Ricci soliton (ARS) (N, g, iii, kappa) on a compact Riemannian manifold (N, g), we use the Ricci curvature in the direction of the potential vector field iii to derive necessary and sufficient conditions for (N, g) to be isometric to a sphere. This expands on several recent results regarding Ricci solitons and almost Ricci solitons by applying specific integral inequalities involving the Ricci curvature evaluated in the direction iii. Furthermore, we present conditions under which iii is either Killing or parallel; in particular, the ARS is trivial.
We study the characteristics of affine vector fields on pseudo-Riemannian manifolds and provide tensorial formulas that characterize these vector fields. Using our approach, we present a…
Considering an almost Ricci soliton (ARS) (N, g, iii, kappa) on a compact Riemannian manifold (N, g), we use the Ricci curvature in the direction of the potential vector field iii to derive…
In this paper, we examine torse-forming vector fields to characterize extrinsic spheres (that is, totally umbilical hypersurfaces with nonzero constant mean curvatures) in Riemannian and…