On oriented Riemannian n-manifold, * : Lambda^k -> Lambda^(n-k) defined via inner-product and volume form; Laplacian on forms Delta = d d* + d* d; Hodge decomposition.
On oriented Riemannian n-manifold, * : Lambda^k -> Lambda^(n-k) defined via inner-product and volume form; Laplacian on forms Delta = d d* + d* d; Hodge decomposition.