Some Geometrical Aspects of Einstein, Ricci and Yamabe Solitons

Abstract

Under certain assumptions, we characterize the almost $\eta$-Einstein, $\eta$-Ricci and $\eta$-Yamabe solitons on a pseudo-Riemannian manifold when the potential vector field of the soliton is infinitezimal harmonic or torse-forming. Moreover, in the second case, if the manifold is Ricci symmetric of constant scalar curvature, then the soliton is completely determined.