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arXiv · 0810.0164

The Hermitian Laplace Operator on Nearly Kähler Manifolds

Andrei Moroianu·Uwe Semmelmann
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Abstract

The moduli space 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. Using the Hermitian Laplace operator and some representation theory, we compute the space 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)=SU_3/T^2, which carries an 8-dimensional moduli space of infinitesimal nearly Kähler deformations, modeled on the Lie algebra su_3 of the isometry group.

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Andrei Moroianu, Uwe Semmelmann. 2009-12-14. The Hermitian Laplace Operator on Nearly Kähler Manifolds. https://doi.org/10.1007/s00220-009-0903-4

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