I am familiar with the notion of Hodge decomposition of an arbitrary differential form into an exact form, a co-exact form, and a harmonic form. Given a curved space with a connection, could you extend the concept of Hodge decomposition by promoting the exterior derivative and codifferential to their covariant counterparts?
2026-03-27 08:42:00.1774600920
Hodge decomposition on a manifold with a nontrivial connection
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