Work

Rigidity of almost Ricci solitons on compact Riemannian manifolds

Year: 2025

Type: article

Abstract: Considering an almost Ricci soliton (ARS) $ \left(N, g, \eta, \kappa \right) $ on a compact Riemannian manifold $ (N, g) $, we use the Ricci curvature in the direction of the potential vector field $ \eta $ 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 $ \eta $. Furthermore, we present conditions under which $ \eta $ is either Killing or parallel; in particular, the ARS is trivial.

Source: AIMS Mathematics

DOI: 10.3934/math.2025608

Authors: Mohammed Guediri, Norah Alshehri

Institution: King Saud University

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funder: King Saud University