Almost η-ricci and almost η-yamabe solitons with torse-forming potential vector field

Abstract

We provide properties of almost eta-Ricci and almost eta-Yamabe solitons on submanifolds isometrically immersed into a Riemannian manifold ((M) over tilde, (g) over tilde) whose potential vector field is the tangential component of a torse-forming vector field on (M) over tilde, treating also the case of a minimal or pseudo quasi-umbilical hypersurface. Moreover, we give necessary and sufficient conditions for an orientable hypersurface of the unit sphere to be an almost eta-Ricci or an almost eta-Yamabe soliton in terms of the second fundamental tensor field.