2 problems

Let $(M^n,g,f)$ be an $n$-dimensional compact Vacuum Static Space, meaning that $(M^n,g)$ is an $n$-dimensional Riemannian manifold and $f$ is a non-constant smooth function satisf…

Let $(M,g)$ be a compact vacuum static space, meaning that there is a non-trivial smooth function $f$ satisfying … where $D_gdf$ is the Hessian, $r_g$ is the Ricci tensor, and…