2017/10/20 by Gabjin Yun, Yun, Gabjin, Seungsu Hwang +1 · 1 citation
Physics and Astronomy · Mathematics · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Black Holes and Theoretical Physics
paper · pdf · doi:10.48550/arxiv.1710.08293
On a compact n-dimensional manifold M, it is well known that a critical metric of the total scalar curvature, restricted to the space of metrics with unit volume, is Einstein. It has been conjectured that a critical metric of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of unit volume, will also be Einstein. It was shown that this conjecture is true when M together with a critical metric has harmonic curvature or the metric is Bach flat. In this paper, we tried to prove this conjecture with a divergence-free Bach tensor.