2010/02/09 by David Baraglia, Baraglia, David · 3 citations
Mathematics · #53C07 #53C29 #53C38 #53C43 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53C07 #msc:53C29 #msc:53C38 #msc:53C43
paper · pdf · doi:10.48550/arxiv.1002.1767
Thesis 149 pages, minor corrections
openalex publication_date 2010/02/09 · arxiv created 2010/07/01 · arxiv updated 2010/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the Hitchin component in the space of representations of the fundamental group of a Riemann surface into a split real simple Lie group in the rank 2 case. We prove that such representations are described by a conformal structure and class of Higgs bundle we call cyclic and we show cyclic Higgs bundles correspond to a form of the affine Toda equations. In each case we relate cyclic Higgs bundles to geometric structures on the surface. We elucidate the geometry of generic 2-plane distributions in 5 dimensions, relating it to a parabolic geometry associated to the split real form of G2 and a conformal geometry with holonomy in G2. We prove the distribution is the bundle of maximal isotropics corresponding to the annihilator of a spinor satisfying the twistor-spinor equation. We study the moduli space of coassociative submanifolds of a G2-manifold with an aim towards understanding coassociative fibrations. We consider coassociative fibrations where the fibres are orbits of a T4-action of isomorphisms and prove a local equivalence to minimal 3-manifolds in R3,3≅ H2(T4,ℝ) with positive induced metric.