Deformation theory of nearly Kähler manifolds

Abstract

Nearly Kähler manifolds are the Riemannian 6-manifolds admitting real Killing spinors. Equivalently, the Riemannian cone over a nearly Kähler manifold has holonomy contained in G2. In this paper we study the deformation theory of nearly Kähler manifolds, showing that it is obstructed in general. More precisely, we show that the infinitesimal deformations of the homogeneous nearly Kähler structure on the flag manifold are all obstructed to second order.

References in corpus (3)

• New G2 holonomy cones and exotic nearly Kaehler structures on the 6-sphere and the product of a pair of 3-spheres
• Deformations of nearly Kähler instantons
• Deformations of asymptotically cylindrical G_2 manifolds

Cited by in corpus (12)

• Gauge theory on Aloff-Wallach spaces
• Complete non-compact Spin(7) manifolds from self-dual Einstein 4-orbifolds
• Second order deformations of associative submanifolds in nearly parallel $G_2$-manifolds
• Rate of asymptotic convergence near isolated singularity of G${}_2$ manifold
• Deformation theory of nearly ${\mathrm{G}}_2$ manifolds
• Toric Nearly Kähler manifolds
• The asymptotic geometry of ${\mathrm{G}}_2$-monopoles
• Linear Instability of Sasaki Einstein and nearly parallel ${\mathrm{G}}_2$ manifolds
• Nearly-Kahler 6-Manifolds of Cohomogeneity Two: Local Theory
• The $G_2$ geometry of $3$-Sasaki structures
• The DT-instanton equation on almost Hermitian 6-manifolds
• On the linear stability of nearly-Kähler $6$-manifolds