Generalized pseudo-Riemannian geometry
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- by Michael Kunzinger and Roland Steinbauer
- Trans. Amer. Math. Soc. 354 (2002), 4179-4199
- DOI: https://doi.org/10.1090/S0002-9947-02-03058-1
- Published electronically: June 3, 2002
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Abstract:
Generalized tensor analysis in the sense of Colombeau’s construction is employed to introduce a nonlinear distributional pseudo-Riemannian geometry. In particular, after deriving several characterizations of invertibility in the algebra of generalized functions, we define the notions of generalized pseudo-Riemannian metric, generalized connection and generalized curvature tensor. We prove a “Fundamental Lemma of (pseudo-) Riemannian geometry” in this setting and define the notion of geodesics of a generalized metric. Finally, we present applications of the resulting theory to general relativity.References
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Bibliographic Information
- Michael Kunzinger
- Affiliation: Department of Mathematics, University of Vienna, Strudlhofg. 4, A-1090 Wien, Austria
- Email: Michael.Kunzinger@univie.ac.at
- Roland Steinbauer
- Affiliation: Department of Mathematics, University of Vienna, Strudlhofg. 4, A-1090 Wien, Austria
- Email: roland.steinbauer@univie.ac.at
- Received by editor(s): August 9, 2001
- Received by editor(s) in revised form: January 31, 2002
- Published electronically: June 3, 2002
- Additional Notes: This work was in part supported by research grant P12023-MAT of the Austrian Science Fund
- © Copyright 2002 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 354 (2002), 4179-4199
- MSC (2000): Primary 46F30; Secondary 46T30, 46F10, 83C05
- DOI: https://doi.org/10.1090/S0002-9947-02-03058-1
- MathSciNet review: 1926870