Besse conjecture with vanishing conditions on the Weyl tensor

Gabjin Yun; Seungsu Hwang

Besse conjecture with vanishing conditions on the Weyl tensor

Differential Geometry 2017-05-05 v2

Authors: Gabjin Yun , Seungsu Hwang

Abstract

On a compact $n$ -dimensional manifold, 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 be Einstein. This conjecture was proposed in 1987 by Besse, but has yet to be proved. In this paper, we prove the Besse conjecture with a weaker condition than harmonic curvature for $n\geq 3$ .

Keywords

Besse conjecture Weyl tensor Einstein metric total scalar curvature compact manifold

Cite

@article{arxiv.1612.09125,
  title  = {Besse conjecture with vanishing conditions on the Weyl tensor},
  author = {Gabjin Yun and Seungsu Hwang},
  journal= {arXiv preprint arXiv:1612.09125},
  year   = {2017}
}

Comments

There are some several gaps in proofs of our results. We think that those gaps could not be recovered soon

Besse conjecture with vanishing conditions on the Weyl tensor

Abstract

Keywords

Cite

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