On an oriented n-dimensional Riemannian manifold, the Hodge star is a linear function which converts alternating differential k-forms to alternating (n - k)-forms. If w is an alternating k-form, its Hodge star is given by w(v_1, ..., v_k) = (^* w)(v_(k + 1), ..., v_n) when v_1, ..., v_n is an oriented orthonormal basis.