Construction of Local Conservation Laws by Generalized Isometric Embeddings of Vector Bundles

Details Construction of Local Conservation Laws by Generalized Isometric Embeddings of Vector Bundles Construction of Local Conservation Laws by Generalized Isometric Embeddings of Vector Bundles

2008-04-16

arxiv.org/abs/0804.2608v2

Mathematics

Differential Geometry

17 Pages

Scientific paper

This article uses Cartan-K\"ahler theory to construct local conservation laws from covariantly closed vector valued differential forms, objects that can be given, for example, by harmonic maps between two Riemannian manifolds. We apply the article's main result to construct conservation laws for covariant divergence free energy-momentum tensors. We also generalize the local isometric embedding of surfaces in the analytic case by applying the main result to vector bundles of rank two over any surface.

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