Communications in Mathematical Physics

, Volume 294, Issue 1, pp 251–272

The Hermitian Laplace Operator on Nearly Kähler Manifolds

Article

DOI: 10.1007/s00220-009-0903-4

Cite this article as:
Moroianu, A. & Semmelmann, U. Commun. Math. Phys. (2010) 294: 251. doi:10.1007/s00220-009-0903-4

Abstract

The moduli space \({\mathcal {NK}}\) of infinitesimal deformations of a nearly Kähler structure on a compact 6-dimensional manifold is described by a certain eigenspace of the Laplace operator acting on co-closed primitive (1, 1) forms (cf. Moroianu et al. in Pacific J Math 235:57–72, 2008). Using the Hermitian Laplace operator and some representation theory, we compute the space \({\mathcal {NK}}\) on all 6-dimensional homogeneous nearly Kähler manifolds. It turns out that the nearly Kähler structure is rigid except for the flag manifold F(1, 2) = SU3/T2, which carries an 8-dimensional moduli space of infinitesimal nearly Kähler deformations, modeled on the Lie algebra \({\mathfrak{su}_3}\) of the isometry group.

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.CMLS, École Polytechnique, UMR 7640 du CNRSPalaiseauFrance
  2. 2.Mathematisches InstitutUniversität zu KölnKölnGermany