Remarks on critical metrics of the scalar curvature and volume functionals on compact manifolds with boundary

H. Baltazar, E. Ribeiro Jr

Published 2017-03-06Version 1

We provide a general B\"ochner type formula which enables us to prove some rigidity results for $V$-static spaces. Moreover, we show that an $n$-dimensional positive static triple with connected boundary and positive scalar curvature must be isometric to the standard hemisphere, provided that the metric has zero radial Weyl curvature and satisfies a suitable pinching condition.