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 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. 143–162DOI 10.4171/ZAA/1282