Hodge theory on nearly Kaehler manifolds

Details Hodge theory on nearly Kaehler manifolds Hodge theory on nearly Kaehler manifolds

2005-10-28

arxiv.org/abs/math/0510618v8

Geometry & Topology 15 (2011) , no. 4, 2111--2133

Mathematics

Differential Geometry

v. 8.0, 22 pages, final version (accepted by G&T), introduction cleaned up a bit

Scientific paper

10.2140/gt.2011.15.2111

Let (M,I, \omega, \Omega) be a nearly Kaehler 6-manifold, that is, an SU(3)-manifold with the (3,0)-form \Omega and the Hermitian form \omega which satisfies $d\omega=3\lambda\Re\Omega, d\Im\Omega=-2\lambda\omega^2$, for a non-zero real constant \lambda. We develop an analogue of Kaehler relations on M, proving several useful identities for various intrinsic Laplacians on M. When M is compact, these identities bring powerful results about cohomology of M. We show that harmonic forms on M admit the Hodge decomposition, and prove that H^{p,q}(M)=0 unless p=q or (p=1, q=2) or (p=2, q=1).

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