nLab
harmonic form

Context

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Riemannian geometry

Contents

Definition

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