Contents Online

# Asian Journal of Mathematics

## Volume 15 (2011)

### Number 4

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

Pages: 521 – 538

DOI: http://dx.doi.org/10.4310/AJM.2011.v15.n4.a2

#### Author

#### 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.

#### Keywords

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

#### 2010 Mathematics Subject Classification

32C22, 37K05, 58A15