A harmonic form on an oriented Riemannian manifold is a differential form 
satisfying 
, where 
is the Hodge
Laplacian. On a compact manifold without
boundary, this is equivalent to 
and 
. On such a compact
manifold, Hodge theory gives each real de Rham
cohomology class a unique harmonic representative.
Harmonic Form
See also
Differential k-Form, Hodge Star, Hodge Theory, LaplacianExplore with Wolfram|Alpha
References
Warner, F. W. Foundations of Differentiable Manifolds and Lie Groups. New York: Springer-Verlag, 1983.Cite this as:
Weisstein, Eric W. "Harmonic Form." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HarmonicForm.html