Isometric immersions into the Minkowski spacetime for Lorentzian manifolds with limited regularity
Classical Analysis and ODEs
2007-12-28 v1 General Relativity and Quantum Cosmology
Differential Geometry
Abstract
Assuming minimal regularity assumptions on the data, we revisit the classical problem of finding isometric immersions into the Minkowski spacetime for hypersurfaces of a Lorentzian manifold. Our approach encompasses metrics having Sobolev regularity and Riemann curvature defined in the distributional sense, only. It applies to timelike, spacelike, or null hypersurfaces with arbitrary signature that possibly changes from point to point.
Keywords
Cite
@article{arxiv.0712.4214,
title = {Isometric immersions into the Minkowski spacetime for Lorentzian manifolds with limited regularity},
author = {Philippe G. LeFloch and Cristinel Mardare and Sorin Mardare},
journal= {arXiv preprint arXiv:0712.4214},
year = {2007}
}
Comments
29 pages