A Gauss-Bonnet Formula for Metrics with Varying Signature | Zendy

Michael Steller | Zendy

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A Gauss-Bonnet Formula for Metrics with Varying Signature

Author(s) -

Michael Steller

Publication year - 2006

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1282

Subject(s) - signature (topology) , gauss , computer science , mathematics , gauss–bonnet theorem , calculus (dental) , artificial intelligence , algorithm , physics , geometry , mathematical physics , medicine , einstein , quantum mechanics , dentistry

A Gauss–Bonnet formula for compact orientable connected Riemannian or Lorentzian 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.

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