Elementary Differential Topology
Hodge decomposition is a fundamental theorem in differential geometry and topology, which states that any smooth differential form on a compact oriented Riemannian manifold can be uniquely decomposed into three distinct components: an exact form, a co-exact form, and a harmonic form. This powerful result connects geometry and analysis by showing how these forms relate to the underlying topological structure of the manifold, particularly in the context of de Rham cohomology groups.
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