Moduli spaces of oriented Type A manifolds of dimension at least 3

TL;DR

This paper studies the structure and symmetry groups of moduli spaces of oriented Type A manifolds with non-degenerate Ricci tensors in dimensions three and higher, revealing phenomena distinct from surface cases.

Contribution

It characterizes the moduli space of oriented Type A manifolds with non-degenerate Ricci tensors in higher dimensions and classifies symmetry groups in dimension three.

Findings

Phenomena differ significantly from surface cases.

Complete classification of symmetry groups in dimension three.

Analysis includes manifolds with and without torsion.

Abstract

We examine the moduli space of oriented locally homogeneous manifolds of Type A which have non-degenerate symmetric Ricci tensor both in the setting of manifolds with torsion and also in the torsion free setting where the dimension is at least 3. These exhibit phenomena that is very different than in the case of surfaces. In dimension 3, we determine all the possible symmetry groups in the torsion free setting.