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

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.

arXiv comment22 pages

References in corpus (10)

• Superstrings with Intrinsic Torsion
• Spinorial description of $\mathrm{SU}(3)$- and $G_2$-manifolds
• Natural connection with totally skew-symmetric torsion on almost contact manifolds with B-metric
• A connection with parallel torsion on almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics
• Canonical bifurcation in higher derivative, higher spin, theories
• Noncompactness and maximum mobility of type III Ricci-flat self-dual neutral Walker four-manifolds
• Comments on HKT supersymmetric sigma models and their Hamiltonian reduction
• Adapted connections on metric contact manifolds
• A method of deforming G-structures
• The moduli space of Type~A surfaces with torsion and non-singular symmetric Ricci tensor

Cited by in corpus (1)

• A natural linear equation in affine geometry: the affine quasi-Einstein equation