Energy-momentum's local conservation laws and generalized isometric embeddings of vector bundles

TL;DR

This paper uses exterior differential systems to solve the generalized isometric embedding problem for vector bundles and constructs conservation laws for certain PDEs, including divergence-free energy-momentum tensors.

Contribution

It provides a positive solution to the generalized isometric embedding problem and demonstrates how to derive conservation laws for specific PDE classes.

Findings

Positive solution to the generalized isometric embedding problem

Construction of conservation laws for divergence-free energy-momentum tensors

Application of exterior differential systems to PDE conservation laws

Abstract

This text is the extended version of a talk given at the conference Geometry, Topology, QFT and Cosmology hold from May 28 to May 30, 2008 at the Observatoire de Paris. Using exterior differential systems, I provide a positive answer to the generalized isometric embedding problem of vector bundles, and show how conservation laws for a class of PDE can be constructed, for instance, for covariant divergence-free energy-momentum tensors.