A simple proof of the Gauss-Bonnet-Chern formula for Finsler manifolds

2013/03/08 by Zhao, Wei
#47A53 #53B40 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1303.1918

Abstract

From the point of view of index theory, we give a simple proof of a Gauss-Bonnet-Chern formula for all Finsler manifolds by the Cartan connection. Based on this, we establish a Gauss-Bonnet-Chern formula for any metric-compatible connection and also derive the Gauss-Bonnet-Chern formula of Lackey.

Related

• Superconnections and An Intrinsic Gauss-Bonnet-Chern Formula for Finsler Manifolds
• The Gauss-Bonnet-Chern Theorem on Riemannian Manifolds
• Adiabatic limit and connections in Finsler Geometry
• Decomposition Theory of Spin Connection and Topological Structure of Gauss-Bonnet-Chern Theorem on Manifold With Boundary
• Chern connection of a pseudo-Finsler metric as a family of affine\n connections