Metric Coordinate Systems
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2007-05-23 v1 度量几何
摘要
Coordinate systems are defined on general metric spaces with the purpose of generalizing vector fields on a manifold. Conversion formulae are available between metric and Cartesian coordinates on a Hilbert space. Nagumo's Invariance Theorem is invoked to prove the analogue of the classical Cauchy-Lipschitz Theorem for vector fields on a locally compact coordinatized space. A metric space version of Nagumo's Theorem is one consequence. Examples are given throughout.
引用
@article{arxiv.math/0206253,
title = {Metric Coordinate Systems},
author = {Craig Calcaterra and Axel Boldt and Michael Green and David Bleecker},
journal= {arXiv preprint arXiv:math/0206253},
year = {2007}
}
备注
31 pages, 2 figures