Gradient Weyl-Ricci Soliton

Abstract

The classical notion of gradient Ricci soliton is extended here to the gradient Weyl-Ricci soliton. A Weylstructure of the base manifold M is lifted to its tangent bundle TM , by using the Sasaki metric. We give some necessaryand sufficient conditions such that the Weyl structure on TM to be a gradient Weyl-Ricci soliton.