Riemannian manifolds with structure group PSU(3)

TL;DR

This paper investigates 8-dimensional Riemannian manifolds with PSU(3)-structure, classifying their intrinsic torsion, analyzing associated differential equations, and exploring their holonomy properties.

Contribution

It provides a classification of PSU(3)-structures on 8-manifolds via intrinsic torsion and characterizes their geometry through differential equations and holonomy analysis.

Findings

Classification of PSU(3)-structures based on intrinsic torsion

Differential equations characterizing structure classes

Analysis of holonomy related to the structure-preserving connection

Abstract

We study 8-dimensional Riemannian manifolds that admit a PSU(3)-structure. We classify these structures by their intrinsic torsion and characterize the corresponding classes via differential equations. Moreover, we consider a connection defined by a 3- and a 4-form that preserves the underlying structure. Finally, we discuss the geometry of these manifolds relatively to the holonomy algebra of this connection.