# nLab harmonic form

cohomology

### Theorems

#### Riemannian geometry

Riemannian geometry

# Contents

## Definition

A differential form $\omega \in {\Omega }^{n}\left(X\right)$ on a Riemannian manifold $\left(X,g\right)$ is called a harmonic fom if it is in the kernel of the Laplace operator ${\Delta }_{g}$ of $X$ in that $\Delta \omega =\left(d+{d}^{†}{\right)}^{2}\omega =0$.

## Properties

The basic properties of harmonic forms are described by Hodge theory. See there for details.

## References

• Springer Online Dictionary, Harmonic form (web)

Revised on February 1, 2011 09:25:37 by Urs Schreiber (89.204.137.77)