Spaces admitting homogeneous G2-structures

Abstract

We classify all seven-dimensional spaces which admit a homogeneous cosymplectic G2-structure. The motivation for this classification is that each of these spaces is a possible principal orbit of a parallel Spin(7)-manifold of cohomogeneity one.

20 pages, no figures

References in corpus (2)

• Cohomogeneity-one G2-structures
• Cohomogeneity one Einstein-Sasaki 5-manifolds

Cited by in corpus (11)

• Closed forms and multi-moment maps
• Exceptional holonomy and Einstein metrics constructed from Aloff-Wallach spaces
• Harmonic flow of geometric structures
• On the automorphism group of a closed G${}_2$-structure
• Special cohomogeneity one metrics with Q^111 or M^110 as principal orbit
• AdS4 backgrounds with N>16 supersymmetries in 10 and 11 dimensions
• Harmonic $Sp(2)$-invariant $G_2$-structures on the $7$-sphere
• Decomposable $(4,7)$ solutions in eleven-dimensional supergravity
• Yang-Mills solutions and Spin(7)-instantons on cylinders over coset spaces with $G_2$-structure
• Homogeneous 8-manifolds admitting invariant Spin(7)-structures
• Coclosed $G_2$-structures on $\text{SU}(2{)}^2$-invariant cohomogeneity one manifolds