New gap results on n‐dimensional static manifolds

Abstract

AbstractIn this note, we obtain new classification results for static and V‐static manifolds under pinching conditions of two different kinds. Firstly, we prove a classification result in higher dimensions assuming a condition of nonnegative Ricci curvature. This extends some recently obtained gap results on the traceless Ricci tensor. Furthermore, we employ the construction of an Einstein manifold associated to a static manifold in order to obtain a classification result in higher dimensions under a pinching condition on the boundary area.