K\"{a}hler identities for almost complex manifolds

Luis Fernandez; Samuel Hosmer

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arXiv · 2208.07276

K\"{a}hler identities for almost complex manifolds

Luis Fernandez·Samuel Hosmer

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Abstract

We obtain a generalization, for a general compact almost complex manifold, of the well-known K\"{a}hler (or Hodge) identities for K\"{a}hler manifolds involving the commutators of the exterior differential and the Lefschetz operator and its adjoint. The main idea is to study the problem on the Clifford bundle via the Dirac operator, and then translate the results to the exterior bundle.

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Luis Fernandez, Samuel Hosmer. 2022-08-15. K\"{a}hler identities for almost complex manifolds. https://arxiv.org/abs/2208.07276

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