A Remark on Chern-Weil Theory

TL;DR

This paper demonstrates that Chern-Weil theory for tensor bundles can be derived from natural closed forms on total spaces of torsion-free connections, providing a new perspective on classical differential geometry.

Contribution

It reveals that Chern-Weil theory follows from the existence of natural closed forms on total spaces of torsion-free connections, linking geometric structures to topological invariants.

Findings

Chern-Weil theory is a consequence of natural closed forms.

Natural closed forms exist on total spaces of torsion-free connections.

This approach offers a new perspective on classical differential geometry.

Abstract

We show that Chern-Weil theory for tensor bundles over manifolds is a consequence of the existence of natural closed differential forms on total spaces of torsion free connections on frame bundles.