This article uses Cartan-K̈ahler 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.
- Cartan-K̈ahler theory
- Conservation laws
- Conservation laws for energy-momentum tensors
- Exterior differential systems
- Generalized isometric embeddings of vector bundles
ASJC Scopus subject areas
- Applied Mathematics