Toric moment mappings and Riemannian structures

TL;DR

This paper explores the relationship between coadjoint orbits of SO(6), Riemannian structures, and moment polytopes, applying the theory to intrinsic torsion varieties on the Iwasawa manifold.

Contribution

It introduces a novel interpretation of symplectic fibrations and moment polytopes in the context of Riemannian G-reductions in six dimensions.

Findings

Characterization of coadjoint orbits as Riemannian reductions

Analysis of symplectic fibrations and moment polytopes

Description of intrinsic torsion varieties on the Iwasawa manifold

Abstract

Coadjoint orbits for the group SO(6) parametrize Riemannian G-reductions in six dimensions, and we use this correspondence to interpret symplectic fibrations between these orbits, and to analyse moment polytopes associated to the standard Hamiltonian torus action on the coadjoint orbits. The theory is then applied to describe so-called intrinsic torsion varieties of Riemannian structures on the Iwasawa manifold.