Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2006-06-30
A Gauss-Bonnet Formula for Metrics with Varying SignatureMichael Steller (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