The moduli space of Type~A surfaces with torsion and non-singular symmetric Ricci tensor

Abstract

We examine the moduli spaces of Type~A connections on oriented and unoriented surfaces both with and without torsion in relation to the signature of the associated symmetric Ricci tensor. If the signature of the symmetric Ricci tensor is (1,1) or (0,2), the moduli spaces are smooth. If the signature is (2,0), there is an orbifold singularity.

References in corpus (7)

• The Srni lectures on non-integrable geometries with torsion
• Special Hermitian metrics on compact solvmanifolds
• Spinorial description of $\mathrm{SU}(3)$- and $G_2$-manifolds
• Homogeneous affine surfaces: affine Killing vector fields and Gradient Ricci solitons
• A classification of locally homogeneous affine connections on compact surfaces
• Adapted connections on metric contact manifolds
• A method of deforming G-structures

Cited by in corpus (2)

• Moduli spaces of oriented Type A manifolds of dimension at least 3
• Moduli spaces of Type~$\mathcal{B}$ surfaces with torsion