Natural Ricci Solitons on Tangent and Unit Tangent Bundles

Abstract

Considering pseudo-Riemannian g-natural metrics on tangent bundles, we prove that the condition of being Ricci soliton is hereditary in the sense that a Ricci soliton structure on the tangent bundle gives rise to a Ricci soliton structure on the base manifold. Restricting ourselves to some class of pseudo-Riemannian g-natural metrics, we show that the tangent bundle is a Ricci soliton if and only if the base manifold is flat and the potential vector field is a complete lift of a conformal vector field. We give then a classification of conformal vector fields on the tangent bundle of a flat Riemannian manifold equipped with these g-natural metrics. When unit tangent bundles over a constant curvature Riemannian manifold are endowed with pseudo-Riemannian Kaluza-Klein type metric, we give a classification of Ricci soliton structures whose potential vector fields are fiber-preserving, inferring the existence of some of them which are non Einstein.

Analyzing Curvature Properties and Geometric Solitons of the Twisted Sasaki Metric on the Tangent Bundle over a Statistical Manifold

“…where M = (M i s ) and N = (N i ) are (1,1) and (1, 0) tensor fields on M n . Substituting Equation (19) in Equation (17), we obtain…”

“…Several authors have explored soliton structures in different contexts. For instance, Abbassi and Amri [19] investigated natural Ricci soliton structures on the tangent and unit tangent bundles of Riemannian manifolds. Chen and Deshmukh [20] introduced the concept of quasi-Yamabe solitons on Riemannian manifolds.…”