The Hermitian Laplace Operator on Nearly Kähler Manifolds

Andrei Moroianu (1) , Uwe Semmelmann (2)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 UNI KOELN - Mathematisches Institut

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.

Mots clés: Nearly Kähler deformations; Hermitian Laplace operator

Domaines: Géométrie différentielle [math.DG]

Andrei Moroianu, Uwe Semmelmann. The Hermitian Laplace Operator on Nearly Kähler Manifolds. Communications in Mathematical Physics, 2009, 294 (1), pp.251-272. ⟨10.1007/s00220-009-0903-4⟩. ⟨hal-00326079v2⟩