Almost η-Ricci and almost η-Yamabe solitons with torse-forming potential vector field

Abstract

We provide properties of almost η-Ricci and almost η-Yamabe solitons on submanifolds isometrically immersed into a Riemannian manifold whose potential vector field is the tangential component of a torse-forming vector field on , 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 η-Ricci or an almost η-Yamabe soliton in terms of the second fundamental tensor field.