On conformal collineation and almost Ricci solitons

TL;DR

This paper explores conditions under which certain Riemannian manifolds with special vector fields are isometric to spheres or Euclidean spaces, and discusses triviality results for almost Ricci solitons with affine conformal Killing potentials.

Contribution

It establishes new criteria linking affine conformal Killing vector fields to the geometric structure of manifolds and analyzes triviality in almost Ricci solitons with such potentials.

Findings

Manifolds with nontrivial closed affine conformal Killing vectors are isometric to spheres or Euclidean spaces.

Provides conditions for triviality of almost Ricci solitons with affine conformal Killing potentials.

Characterizes geometric structures under conformal collineation constraints.

Abstract

We provide conditions for a Riemannian manifold with a nontrivial closed affine conformal Killing vector field to be isometric to a Euclidean sphere or to the Euclidean space. Also, we formulate some triviality results for almost Ricci solitons with affine conformal Killing potential vector field.