1995/01/02 by Quo-Shin Chi, Chi, Quo-Shin, Lorenz Schwachhöfer +2 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #dg-ga #math.DG
paper · pdf · doi:10.48550/arxiv.dg-ga/9501001
30 pages, AMS-TeX, uses pictex
arxiv created 1995/01/02 · openalex publication_date 1995/01/02 · arxiv updated 2016/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Bryant \citeBr proved the existence of torsion free connections with exotic holonomy, i.e. with holonomy that does not occur on the classical list of Berger \citeBer. These connections occur on moduli spaces \Y of rational contact curves in a contact threefold \W. Therefore, they are naturally contained in the moduli space \Z of all rational curves in \W. We construct a connection on \Z whose restriction to \Y is torsion free. However, the connection on \Z has torsion unless both \Y and \Z are flat. We also show the existence of a new exotic holonomy which is a certain sixdimensional representation of \Sl × \Sl. We show that every regular H3-connection (cf. \citeBr) is the restriction of a unique connection with this holonomy.