The generalized Pohozaev-Schoen identity for asymptotically hyperbolic manifolds and its applications

Abstract

In this paper, we establish the generalized Pohozaev-Schoen identity for asymptotically hyperbolic manifolds. As an application, we consider the Einstein-type asymptotically hyperbolic manifolds, especially the case with static potentials. We also consider its application to the asymptotically hyperbolic manifold with B-generalized soliton structure and derive some rigidity result when it admits an almost Ricci soliton structure.