Construction of local conservation laws by generalized isometric embeddings of vector bundles

Nabil Kahouadji*

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)521-538
Number of pages18
JournalAsian Journal of Mathematics
Volume15
Issue number4
DOIs
StatePublished - Dec 2011

Keywords

  • Cartan-K̈ahler theory
  • Conservation laws
  • Conservation laws for energy-momentum tensors
  • Exterior differential systems
  • Generalized isometric embeddings of vector bundles

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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