Hodge identities

A collection of identities which hold on a Kähler manifold, also called the Hodge identities. Let ω be a Kähler form, d = d + d^_ be the exterior derivative, where d^_ is the del bar operator, [A, B] = A B - B A be the commutator of two differential operators, and A^† denote the formal adjoint of A. The following operators also act on differential forms on a Kähler manifold: L(α) | = | α⋀ω Λ(α) | = | L^†(α) = α⌟ω d_c | = | -J d J, where J is the almost complex structure, J^2 = - I, and ⌟ denotes the interior product.

complex manifold | Hodge's theorem | Kähler form | Kähler manifold | Kähler potential | Kähler structure | Riemannian metric | symplectic manifold