## Asian Journal of Mathematics

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

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

#### 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