Three Dimensional Homogeneous Hyperbolic Ricci Solitons

Abstract

Abstract In this paper, we consider the self-similar solutions to the hyperbolic geometric flow, called hyperbolic Ricci solitons. Also, we investigate hyperbolic Ricci solitons on three-dimensional homogeneous manifolds with Riemannian and Lorentzian metrics and obtain some hyperbolic Ricci solitons on such manifolds.