Geometry & Topology
- Geom. Topol.
- Volume 15, Number 4 (2011), 2111-2133.
Hodge theory on nearly Kähler manifolds
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 .
Geom. Topol., Volume 15, Number 4 (2011), 2111-2133.
Received: 19 June 2008
Revised: 7 October 2010
Accepted: 12 June 2011
First available in Project Euclid: 20 December 2017
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Verbitsky, Misha. Hodge theory on nearly Kähler manifolds. Geom. Topol. 15 (2011), no. 4, 2111--2133. doi:10.2140/gt.2011.15.2111. https://projecteuclid.org/euclid.gt/1513732363