English

Proof of Chern's conjecture on affine manifolds

Differential Geometry 2020-07-28 v2

Abstract

We prove an old conjecture of S. S. Chern that the Euler characteristic of a closed affine manifold equals to zero.

Keywords

Cite

@article{arxiv.2002.03105,
  title  = {Proof of Chern's conjecture on affine manifolds},
  author = {Jianquan Ge},
  journal= {arXiv preprint arXiv:2002.03105},
  year   = {2020}
}

Comments

There is a minor error in the Hessian representation in Lemma 2.1. found by Andrea Clini on February 17 (I was aware of this a month later), which maked the author carefully revise the whole paper and find there a key error in the commutation of the limits at the end of the proof. Although this paper is withdrawed now to avoid some misunderstanding, I'm still trying to overcome this error