Vol. 235, No. 1, 2008

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ISSN: 0030-8730
Deformations of nearly Kähler structures

Andrei Moroianu, Paul-Andi Nagy and Uwe Semmelmann

Vol. 235 (2008), No. 1, 57–72
Abstract

We study the space of nearly Kähler structures on compact 6-dimensional manifolds. In particular, we prove that the space of infinitesimal deformations of a strictly nearly Kähler structure (with scalar curvature scal) modulo the group of diffeomorphisms is isomorphic to the space of primitive coclosed (1,1)-eigenforms of the Laplace operator for the eigenvalue 2 scal5.

Keywords
infinitesimal deformations, SU3 structures, nearly Kähler manifolds, Gray manifolds
Mathematical Subject Classification 2000
Primary: 58E30, 53C10, 53C15
Milestones
Received: 7 June 2007
Revised: 10 September 2007
Published: 1 March 2008
Authors
Andrei Moroianu
Centre de Mathématiques
École Polytechnique
91128 Palaiseau Cedex
France
http://www.math.polytechnique.fr/cmat/moroianu/moroianu.html
Paul-Andi Nagy
Department of Mathematics
University of Auckland
Private Bag 92019, Auckland Mail Centre
Auckland 1142
New Zealand
http://www.math.auckland.ac.nz/wiki/Paul_Andi_Nagy
Uwe Semmelmann
Mathematisches Institut
Universität zu Köln
Weyertal 86-90
D-50931 Köln
Germany
http://www.mi.uni-koeln.de/~semmelma/