Manifolds with holonomy U*(2m)

2014/03/27 by Hitchin, Nigel
#53C26 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1403.7133

Abstract

We consider the geometry determined by a torsion-free affine connection whose holonomy lies in the subgroup U*(2m), a real form of GL(2m,C), otherwise denoted by SL(m,H).U(1). We show in particular how examples may be generated from quaternionic Kähler or hyperkähler manifolds with a circle action.

Related

• Recent Advances in the Theory of Holonomy
• Complex connections with trivial holonomy
• Complex quaternionic manifolds and c-projective structures
• Riemannian Holonomy and Algebraic Geometry
• Flat manifolds with holonomy representation of quaternionic type