Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Generalized pseudo-Riemannian geometry


Authors: Michael Kunzinger and Roland Steinbauer
Journal: Trans. Amer. Math. Soc. 354 (2002), 4179-4199
MSC (2000): Primary 46F30; Secondary 46T30, 46F10, 83C05
Published electronically: June 3, 2002
MathSciNet review: 1926870
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 46F30, 46T30, 46F10, 83C05

Retrieve articles in all journals with MSC (2000): 46F30, 46T30, 46F10, 83C05


Additional 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

DOI: http://dx.doi.org/10.1090/S0002-9947-02-03058-1
PII: S 0002-9947(02)03058-1
Keywords: Algebras of generalized functions, Colombeau algebras, generalized tensor fields, generalized metric, (generalized) pseudo-Riemannian geometry, general relativity.
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
Article copyright: © Copyright 2002 American Mathematical Society