The Hermitian Laplace Operator on Nearly Kähler Manifolds

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.

23 pages

References in corpus (3)

• Unit Killing Vector Fields on Nearly Kahler Manifolds
• Infinitesimal Einstein Deformations of Nearly Kähler Metrics
• Nearly Kaehler and nearly parallel G_2-structures on spheres

Cited by in corpus (14)

• Deformation theory of nearly Kähler manifolds
• Generalized Killing spinors and Lagrangian graphs
• Deformation theory of G_2 conifolds
• Infinitesimal Einstein Deformations of Nearly Kähler Metrics
• Deformations of nearly Kähler instantons
• The kernel of the Rarita-Schwinger operator on Riemannian spin manifolds
• Deformations of Asymptotically Conical $G_2$-Instantons
• Deformations of asymptotically conical Spin(7)-manifolds
• Deformations of ${\mathrm{G}}_2$-instantons on nearly ${\mathrm{G}}_2$ manifolds
• Rate of asymptotic convergence near isolated singularity of G${}_2$ manifold
• Jacobi relations on naturally reductive homogeneous spaces
• Toric Nearly Kähler manifolds
• G${}_2$ manifolds with nodal singularities along circles
• On the linear stability of nearly-Kähler $6$-manifolds