# A Gauss-Bonnet Formula for Metrics with Varying Signature

### Michael Steller

Universität Stuttgart, Germany

## Abstract

A Gauss–Bonnet formula for compact orientable connected Riemannian or Lorentz-ian 2-manifolds is well-known. We investigate singular metrics on 2-manifolds with varying signature. Such metrics are necessarily degenerate at some points of $M$ where most of the usual definitions for geometric quantities break down. We prove that under some additional assumptions there is a Gauss–Bonnet formula for compact orientable connected 2-manifolds with a singular metric. Some examples are given.

## Cite this article

Michael Steller, A Gauss-Bonnet Formula for Metrics with Varying Signature. Z. Anal. Anwend. 25 (2006), no. 2, pp. 143–162

DOI 10.4171/ZAA/1282