Almost Yamabe solitons satisfying certain conditions on the associated vector field

Abstract

We study an almost Yamabe soliton (Mⁿ, g, V, ρ) and obtain various conditions on V in terms of infinitesimal harmonic transformation, 2-Killing, and an inequality, to show that V is Killing. In addition, we have provided characterizations of a 2-Killing vector field V on any Riemannian manifold in terms of the strain tensor and divergence of V .