Volume 15, issue 4 (2011)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 26
Issue 7, 2855–3306
Issue 6, 2405–2853
Issue 5, 1907–2404
Issue 4, 1435–1905
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Hodge theory on nearly Kähler manifolds

Misha Verbitsky

Geometry & Topology 15 (2011) 2111–2133
Abstract

Let (M,I,ω,Ω) be a nearly Kähler 6–manifold, that is, an SU(3)–manifold with (3,0)–form Ω and Hermitian form ω which satisfies dω = 3λReΩ, dImΩ = 2λω2 for a nonzero real constant λ. We develop an analogue of the Kähler relations on M, proving several useful identities for various intrinsic Laplacians on M. When M is compact, these identities give powerful results about cohomology of  M. We show that harmonic forms on M admit a Hodge decomposition, and prove that Hp,q(M) = 0 unless p = q or (p = 1,q = 2) or (p = 2,q = 1).

Keywords
nearly Kähler, $G_2$–manifold, Hodge decomposition, Hodge structure, Calabi–Yau manifold, almost complex structure, holonomy
References
Publication
Received: 19 June 2008
Revised: 7 October 2010
Accepted: 12 June 2011
Published: 28 October 2011
Proposed: Gang Tian
Seconded: Simon Donaldson, Yasha Eliashberg
Authors
Misha Verbitsky
Laboratory of Algebraic Geometry
Faculty of Mathematics, NRU HSE
7 Vavilova Ul
Moscow 117312
Russia
http://verbit.ru/