SO(3)-Structures on 8-manifolds

TL;DR

This paper investigates 8-dimensional Riemannian manifolds with SO(3) symmetry, analyzing their geometric structures and connections to quaternionic and related geometries through representation theory.

Contribution

It provides a detailed study of SO(3)-structures on 8-manifolds and clarifies their relation to quaternionic and other geometric frameworks using representation-theoretic methods.

Findings

Characterization of tangent space decomposition into 3- and 5-dimensional irreducible parts.

Connections established between SO(3)-structures and quaternionic, almost product, and PSU geometries.

Representation-theoretic analysis elucidates geometric relationships.

Abstract

We study Riemannian 8-manifolds with an infinitesimal action of SO(3) by which each tangent space breaks into irreducible spaces of dimensions 3 and 5. The relationship with quaternionic, almost product- and PSU-geometry is thoroughly explained using representation-theoretical arguments.