Sp(3) structures on 14-dimensional manifolds

TL;DR

This paper explores the existence and uniqueness of Sp(3) structures on 14-dimensional manifolds, providing topological criteria, constructing examples, and clarifying connections on Lie groups.

Contribution

It introduces topological conditions for Sp(3) structures, constructs homogeneous examples, and unifies different types of connections on Lie groups.

Findings

Derived topological criteria for Sp(3) structures

Constructed large families of homogeneous examples

Proved uniqueness of characteristic connections and their equivalence on Lie groups

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.