Revisiting 3-Sasakian and $G_2$-structures

Abstract

The algebra of exterior differential forms on a regular 3-Sasakian 7-manifold is investigated, with special reference to nearly-parallel $G_2$ 3-forms. This is applied to the study of 3-forms invariant under cohomogeneity-one actions by $SO(4)$ on the 7-sphere and on Berger's space $SO(5)/SO(3)$.

21 pages

References in corpus (7)

• New G2 holonomy cones and exotic nearly Kaehler structures on the 6-sphere and the product of a pair of 3-spheres
• 3-Sasakian manifolds in dimension seven, their spinors and G_2 structures
• Nearly hypo structures and compact Nearly Kähler 6-manifolds with conical singularities
• Associative Submanifolds of the 7-Sphere
• Some associative submanifolds of the squashed 7-sphere
• Killing and twistor spinors with torsion
• Geometric Flows of $G_2$-Structures on 3-Sasakian 7-Manifolds