Generalized pseudo-Riemannian geometry

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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.
23 pages, Latex, final form

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Functional Analysis, General Relativity and Quantum Cosmology, Differential Geometry, Primary: 46F30; secondary: 46T30, 46F10, 83C05

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http://salesiana.dossiersoluciones.com/handle/123456789/61817

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0107057
 http://arxiv.org/abs/math/0107057
 Trans. Amer. Math. Soc. 354 (2002), no. 10, 4179-4199

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arXiv