Robinson manifolds as the Lorentzian analogs of Hermite manifolds
| Autor: | Andrzej Trautman, Pawel Nurowski |
|---|---|
| Rok vydání: | 2002 |
| Předmět: |
Mathematics - Differential Geometry
Invariant manifold FOS: Physical sciences 32C81 53B30 32V30 83C20 Riemannian geometry Causality conditions Pseudo-Riemannian manifold Volume form symbols.namesake General Relativity and Quantum Cosmology Lorentz manifolds Global analysis Ricci-flat manifold FOS: Mathematics Mathematics::Symplectic Geometry Mathematical Physics Hyperkähler manifold Mathematical physics Mathematics Robinson manifolds Twistor bundles Mathematical analysis Mathematical Physics (math-ph) Hermite manifolds Differential Geometry (math.DG) Computational Theory and Mathematics symbols Mathematics::Differential Geometry Geometry and Topology Analysis |
| Zdroj: | Differential Geometry and its Applications. 17(2-3):175-195 |
| ISSN: | 0926-2245 |
| DOI: | 10.1016/s0926-2245(02)00106-7 |
| Popis: | A Lorentzian manifold is defined here as a smooth pseudo-Riemannian manifold with a metric tensor of signature ((2n +1, 1)). A Robinson manifold is a Lorentzian manifold (M) of dimension (\geqslant 4) with a subbundle (N) of the complexification of (TM) such that the fibers of (N\to M) are maximal totally null (isotropic) and ([\Sec N, \Sec N]\subset \Sec N). Robinson manifolds are close analogs of the proper Riemannian, Hermite manifolds. In dimension 4, they correspond to space-times of general relativity, foliated by a family of null geodesics without shear. Such space-times, introduced in the 1950s by Ivor Robinson, played an important role in the study of solutions of Einstein's equations: plane and sphere-fronted waves, the G\"odel universe, the Kerr solution, and their generalizations, are among them. In this survey article, the analogies between Hermite and Robinson manifolds are presented in considerable detail. |
| Databáze: | OpenAIRE |
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