## Asian Journal of Mathematics

### Harmonic forms on principal bundles

Corbett Redden

#### Abstract

We show a relationship between Chern–Simons 1- and 3-forms and harmonic forms on a principal bundle. Doing so requires one to consider an adiabatic limit. For the 3-form case, assume that $G$ is simple and the corresponding Chern–Weil 4-form is exact. Then, the Chern–Simons 3-form on the princpal bundle $G$-bundle, minus a canonical term from the base, is harmonic in the adiabatic limit.

#### Article information

Source
Asian J. Math., Volume 16, Number 4 (2012), 637-660.

Dates
First available in Project Euclid: 12 December 2012

https://projecteuclid.org/euclid.ajm/1355321982

#### Citation

Redden, Corbett. Harmonic forms on principal bundles. Asian J. Math. 16 (2012), no. 4, 637--660. https://projecteuclid.org/euclid.ajm/1355321982