Hyperbolic Ricci solitons on K-contact manifolds and its applications in spacetimes

The aim of the present article is delve into characterizations of hyperbolic Ricci solitons which bear wave characters of K-contact metrics and associated curvatures of manifolds as self similar solutions of a hyperbolic Ricci flow. Also, we investigate gradient hyperbolic Ricci solitons on ?-Einstein K-contact manifolds and construct an example to verify the deduced results. Finally we analyze hyperbolic Ricci solitons in the framework of quasi-Einstein spacetimes.