A note on the Gauss-Bonnet-Chern theorem for general connection
Differential Geometry
2015-12-09 v2 Mathematical Physics
math.MP
Abstract
In this paper, we prove a local index theorem for the DeRham Hodge-laplacian which is defined by the connection compatible with metric. This connection need not be the Levi-Civita connection. When the connection is Levi-Civita connection, this is the classical local Gauss-Bonnet-Chern theorem.
Keywords
Cite
@article{arxiv.1408.3171,
title = {A note on the Gauss-Bonnet-Chern theorem for general connection},
author = {Haoyan Zhao},
journal= {arXiv preprint arXiv:1408.3171},
year = {2015}
}