Asian Journal of Mathematics

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

Nabil Kahouadji

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Abstract

This article uses Cartan–Kähler 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.

Article information

Source
Asian J. Math. Volume 15, Number 4 (2011), 521-538.

Dates
First available in Project Euclid: 12 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1331583346

Mathematical Reviews number (MathSciNet)
MR2853647

Zentralblatt MATH identifier
1248.58003

Subjects
Primary: 58A15: Exterior differential systems (Cartan theory) 37K05: Hamiltonian structures, symmetries, variational principles, conservation laws 32C22: Embedding of analytic spaces

Keywords
Conservation laws generalized isometric embeddings of vector bundles exterior differential systems Cartan–Kähler theory conservation laws for energy-momentum tensors

Citation

Kahouadji, Nabil. Construction of Local Conservation Laws by Generalized Isometric Embeddings of Vector Bundles. Asian J. Math. 15 (2011), no. 4, 521--538.https://projecteuclid.org/euclid.ajm/1331583346


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