nLab
harmonic form

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 $\Delta \omega =(d+d^{†}{)}^2\omega =0$.

Properties

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

References

• Springer Online Dictionary, Harmonic form (web)