| dbp:mathStatement
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- Let be a compact Kähler manifold. Then the de Rham cohomology of admits an orthogonal direct sum decomposition
This decomposition is compatible with the Hodge decomposition into Dolbeault cohomology groups:
In addition
* If , then .
* The map is injective for , and restricts to give an injection for each such that .
* The map is bijective for , and restricts to give a bijection for each such that .
* If , then , and furthermore . (en)
- Let be a Kähler manifold. Then the following identities hold:
* .
* .
*.
*.
* .
* .
* .
*.
*.
* commutes with all of and . It also commutes with and hence preserves bidegree .
Furthermore the operators and satisfy the identities:
* .
* .
* .
* . (en)
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