nLab harmonic form

Context

Riemannian geometry

Riemannian geometry

Contents

Definition

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

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)