Generalized pseudo-Riemannian geometry
| dc.creator | Kunzinger, Michael | |
| dc.creator | Steinbauer, Roland | |
| dc.date | 2001-07-07 | |
| dc.date | 2002-10-31 | |
| dc.date.accessioned | 2026-07-07T04:42:31Z | |
| dc.date.available | 2026-07-07T04:42:31Z | |
| dc.description | 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. | |
| dc.description | 23 pages, Latex, final form | |
| dc.identifier | https://arxiv.org/abs/math/0107057 | |
| dc.identifier | http://arxiv.org/abs/math/0107057 | |
| dc.identifier | Trans. Amer. Math. Soc. 354 (2002), no. 10, 4179-4199 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61817 | |
| dc.subject | Functional Analysis | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.subject | Differential Geometry | |
| dc.subject | Primary: 46F30; secondary: 46T30, 46F10, 83C05 | |
| dc.title | Generalized pseudo-Riemannian geometry | |
| dc.type | text |