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# Zeitschrift für Analysis und ihre Anwendungen

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**Volume 25, Issue 2, 2006, pp. 143–162**

**DOI: 10.4171/ZAA/1282**

Published online: 2006-06-30

A Gauss-Bonnet Formula for Metrics with Varying Signature

Michael Steller^{[1]}(1) Universität Stuttgart, Germany

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.

*Keywords: *Gauss-Bonnet formula, singular metric, pseudo-geodesic, generic metric

Steller Michael: A Gauss-Bonnet Formula for Metrics with Varying Signature. *Z. Anal. Anwend.* 25 (2006), 143-162. doi: 10.4171/ZAA/1282