TOTAL SCALAR CURVATURE AND HARMONIC CURVATURE

By G. Yun, Jeongwook Chang, Seungsu Hwang. 2011

52 citations recorded by the source corpus.

On a compact $n$-dimensional manifold, it has been conjectured that a critical point metric of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of unit volume, will be Einstein. This conjecture was proposed in 1984 by Besse, but has yet to be proved. In this paper, we prove that if the manifold with the critical point metric has harmonic curvature, then it is isometric to a standard sphere.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/fbf025cf16737edeae5febc756b078abdd38ec88

How researchers see this paper

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In Applied Mathematics

1. A. Barros
2. E. Ribeiro
3. Wei Yuan
4. J. Qing

In Astronomy and Astrophysics

1. A. Barros
2. E. Ribeiro
3. Wei Yuan
4. J. Qing

In Geometry and Topology

1. A. Barros
2. E. Ribeiro
3. Wei Yuan
4. J. Qing

Citations in the corpus

• A note on static spaces and related problems (2012, methodology): “Recently Chang, Hwang, and Yun in [4] verified Conjecture 1.”
• Critical point equation on four‐dimensional compact manifolds (2014, background): “More exactly, the goal of this paper is to prove that in 4-dimensional manifolds the assumption that ( M4, g ) is locally conformally flat, considered in [15] and [5], can be replaced by the weaker condition that ( M4, g ) is half conformally flat.”