Sp(3) structures on 14-dimensional manifolds

Abstract

The present article investigates Sp(3) structures on 14-dimensional Riemannian manifolds, a continuation of the recent study of manifolds modeled on rank two symmetric spaces (here: SU(6)/Sp(3)). We derive topological criteria for the existence of such a structure and construct large families of homogeneous examples. As a by-product, we prove a general uniqueness criterion for characteristic connections of G structures and that the notions of biinvariant, canonical, and characteristic connections coincide on Lie groups with biinvariant metric.

24 pages

References in corpus (4)

• On types of non-integrable geometries
• Homogeneity rank of real representations of compact Lie groups
• Twistorial eigenvalue estimates for generalized Dirac operators with torsion
• Riemannian manifolds with structure group PSU(3)

Cited by in corpus (5)

• Spinorial description of $\mathrm{SU}(3)$- and $G_2$-manifolds
• Killing and twistor spinors with torsion
• Invariant connections and $\nabla$-Einstein structures on isotropy irreducible spaces
• The classification of naturally reductive homogeneous spaces in dimensions $n\le 6$
• Deformations of ${\mathrm{G}}_2$-instantons on nearly ${\mathrm{G}}_2$ manifolds