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利用解析延拓证明不定号度量的Chern-Gauss-Bonnet定理

微分几何 2014-09-18 v2

作者: P. Gilkey , J. H. Park

在 arXiv 上查看 ↗ PDF ↗

摘要

我们通过考察切空间上复“度量”的Pfaffian相关的Euler-Lagrange方程，然后应用解析延拓，从黎曼情形的相应结果推导出伪黎曼背景下具有光滑非退化边界的流形的Chern-Gauss-Bonnet定理。

关键词

Chern-Gauss-Bonnet定理不定号度量解析延拓伪黎曼流形边界 Euler-Lagrange方程

引用

@article{arxiv.1405.7613,
  title  = {A proof of the Chern-Gauss-Bonnet theorem for indefinite signature metrics using analytic continuation},
  author = {P. Gilkey and J. H. Park},
  journal= {arXiv preprint arXiv:1405.7613},
  year   = {2014}
}

备注

This paper has been withdrawn by the authors. A later improved version is available upon request from the authors but will not be posted to the arXiv