Chapter 20 Differential Operators on Semi‐Riemannian Manifolds

20.1 Hodge Star

Let images be an oriented semi‐Riemannian m‐manifold of index v, and let Ω M be its volume form. Hodge star is the family of linear maps


defined for 0 ≤ s ≤ m that is the manifold version of Hodge star for scalar product spaces, as discussed in Section 8.5. Thus, for each form ω in Λ s (M), we have a unique form ⋆(ω) in Λ m − s (M) such that


for all forms ξ in Λ m − s (M).

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