A proof of the Chern-Gauss-Bonnet theorem for indefinite signature metrics using analytic continuation

P. Gilkey; J. H. Park

A proof of the Chern-Gauss-Bonnet theorem for indefinite signature metrics using analytic continuation

Differential Geometry 2014-09-18 v2

Authors: P. Gilkey , J. H. Park

Abstract

We derive the Chern-Gauss-Bonnet Theorem for manifolds with smooth non-degenerate boundary in the pseudo-Riemannian context from the corresponding result in the Riemannian setting by examining the Euler-Lagrange equations associated to the Pfaffian of a complex "metric" on the tangent space and then applying analytic continuation.

Keywords

Chern-Gauss-Bonnet theorem indefinite signature metric analytic continuation pseudo-Riemannian manifold boundary Euler-Lagrange equations

Cite

@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}
}

Comments

This paper has been withdrawn by the authors.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

A proof of the Chern-Gauss-Bonnet theorem for indefinite signature metrics using analytic continuation

Abstract

Keywords

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