Results of Hyperbolic Ricci Solitons

We obtain some properties of a hyperbolic Ricci soliton with certain types potential vector fields, and we point out conditions when it reduces to trivial soliton. also study those submanifolds whose fields are the tangential components concurrent field on ambient manifold, in particular, show that totally umbilical is an Einstein manifold. prove if hypersurface Riemannian manifold constant curvature endowed has parallel shape operator, then metallic-shaped hypersurface, determine for be minimal. Moreover, pseudosymmetric hypersurface.