The Hermitian Laplace Operator on Nearly Kähler Manifolds

Communications in Mathematical Physics (Impact Factor: 2.09). 02/2010; 294(1). DOI: 10.1007/s00220-009-0903-4
Source: OAI


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.

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Available from: Andrei Moroianu
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