Métricas críticas do funcional volume fracamente Einstein e variedades com tensores de divergência nula - Oliveira, Fabricio de Figueredo (2018)
We studied critical points of the functional volume in onboard varieties and the functional total scalar curvature in varieties with no board. We prove that under a signal condition in the scalar curvature and with the hypothesis that an n dimensional manifold is weakly Einstein it is possible to classify Miao-Tam Critical Metrics as geodesic balls in shape spaces. Then we prove that the Cotton tensor is always zero when there is zero divergence and we improve some classic results on the CPE conjecture like Yun (2014) besides giving a simpler proof than Santos (2017) for the CPE conjecture when the second divergence of Weyl is null.