A Note on Generalized Solitons

In this paper, we initiate the study of a generalized soliton on Riemannian manifold, find characterization for Euclidean space, and in compact case, sufficient condition under which it reduces to quasi-Einstein manifold. We also conditions an Einstein Note that Ricci solitons being self-similar solutions heat flow, topic is related symmetry geometry manifolds. Moreover, generalizations are naturally symmetry.