Construction of local conservation laws by generalized isometric embeddings of vector bundles (Q428178)

The author proves a result similar to the Cartan-Janet isometric embedding theorem. Over a Riemannian manifold of dimension \(n\), he considers a real vector bundle \(V\) with a real analytic metric and a compatible real analytic connection. On this manifold, take any nowhere vanishing \(V\)-valued covariant constant differential form \(\omega\) of degree \(n-1\). The author proves that near each point of the manifold, the vector bundle admits a local real analytic embedding into a flat vector bundle, say \(W\), so that the \(W\)-valued differential form induced by \(\omega\) is closed. He provides applications to harmonic maps and to the study of energy-momentum tensors in general relativity.