Eigenform

An eigenform of a differential operator on differential forms is a nonzero form such that

(1)

for some constant . For example, on the standard flat torus , with -periodic coordinates and and Riemannian metric , the Dirac operator , where is the exterior derivative and is its formal adjoint with respect to this Riemannian metric, acts on the form

(2)

giving

(3)

i.e., .