Some rigidity results on non-compact almost Ricci solitons

Abstract

We extend well-known results on the rigidity of compact almost Ricci solitons $(M,g,V,\lambda )$ to the complete case by imposing certain conditions on the potential vector field V, regularity constraints on the dilation function λ, and curvature restrictions on M. We also provide another proof with a stronger conclusion of a rigidity result of Costa-Filho for a closed almost Ricci soliton.