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Communications in Mathematical Physics

, Volume 294, Issue 1, pp 251–272 | Cite as

The Hermitian Laplace Operator on Nearly Kähler Manifolds

  • Andrei Moroianu
  • Uwe Semmelmann
Article

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/T 2, which carries an 8-dimensional moduli space of infinitesimal nearly Kähler deformations, modeled on the Lie algebra \({\mathfrak{su}_3}\) of the isometry group.

Keywords

Manifold Laplace Operator Maximal Torus Twistor Space Killing Spinor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

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

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