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

equation

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

equation

for all forms ξ in Λ m − s (M).

Get Semi-Riemannian Geometry now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.