 Hodge star operator

On an oriented Riemannian $n$-manifold, the Hodge star is determined byIt maps $p$-forms to $(n-p)$-forms and satisfies ${\ast }^2=(-1{)}^{p(n-p)}$ on $p$-forms.

The Hodge star operator is a mathematical operator used extensively in differential geometry and algebraic topology, particularly in the context of differential forms on Riemannian manifolds. It acts on differential forms and is used to relate forms of different degrees.