A note on the Gauss-Bonnet-Chern theorem for general connection

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.

References in corpus (2)

• A Gauss-Bonnet-Chern theorem for Finsler vector bundles
• Heat trace asymptotics and the Gauss-Bonnet Theorem for general connections