Conformal vector fields and geometric solitons on the tangent bundle with the ciconia metric

Abstract

Let $(X_{2k},\digamma ,g)$ be an almost anti-paraHermitian manifold with analmost paracomplex structure $\digamma $ and a Riemannian metric $g$ and let $TX$ be its tangent bundle with the ciconia metric $\tilde{g}$. The purposeof this paper is divided into two folds. The first one is to examine the curvature properties of the tangent bundle $TX$ with the ciconia metric $\tilde{g}$. The second oneis to study conformal vector fields and almost Ricci and Yamabe solitons on the tangent bundle $TX$ according to the ciconia metric $\tilde{g}$.