Synectic lift metrics on tangent bundles: exploring soliton structures and gradient variants

Let T M be the tangent bundle with the synectic lift on the n-dimensional Riemannian manifold M . The objective of this article is to investigate the properties of Ricci soliton and generalized Ricci-Yamabe soliton structures according to the synectic lift metric on the tangent bundle T M . Furthermore, the properties of the gradient Ricci soliton and the generalized gradient Ricci-Yamabe soliton are also investigated in this article.