Abstract
Let be a nearly Kähler –manifold, that is, an –manifold with –form and Hermitian form which satisfies , for a nonzero real constant . We develop an analogue of the Kähler relations on , proving several useful identities for various intrinsic Laplacians on . When is compact, these identities give powerful results about cohomology of . We show that harmonic forms on admit a Hodge decomposition, and prove that unless or or .
Citation
Misha Verbitsky. "Hodge theory on nearly Kähler manifolds." Geom. Topol. 15 (4) 2111 - 2133, 2011. https://doi.org/10.2140/gt.2011.15.2111
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