Moduli spaces of Type~$\mathcal{B}$ surfaces with torsion

TL;DR

This paper studies the structure and classification of moduli spaces of Type~$ ext{B}$ surfaces with torsion, focusing on cases with non-degenerate symmetric Ricci tensor, and explores their affine symmetries.

Contribution

It characterizes the moduli spaces of Type~$ ext{B}$ surfaces with torsion and non-degenerate Ricci tensor, and analyzes their affine Killing vector fields.

Findings

Characterization of moduli spaces of Type~$ ext{B}$ surfaces with torsion.

Determination of affine Killing vector fields for these surfaces.

Insights into the geometric structure of these moduli spaces.

Abstract

We examine moduli spaces of locally homogeneous surfaces of Type~$\mathcal{B}$ with torsion where the symmetric Ricci tensor is non-degenerate. We also determine the space of affine Killing vector fields in this context.