(Pluri)harmonic morphisms and the Penrose-Ward transform

2015/02/23 by Radu Pantilie, Pantilie, Radu
Mathematics · Physics and Astronomy · #53C28 #53C43 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AG #math.DG #math.MP #msc:53C28 #msc:53C43

paper · pdf · doi:10.48550/arxiv.1502.06420

Preprint, I.M.A.R., Bucharest, 2015, 19 pages

arxiv created 2015/03/09 · arxiv updated 2015/03/10

Abstract

We show that, in quaternionic geometry, the Ward transform is a manifestation of the functoriality of the basic correspondence between the ρ-quaternionic manifolds and their twistor spaces. We apply this fact, together with the Penrose transform, to obtain existence results for hypercomplex manifolds and for harmonic morphisms from hyper-Kaehler manifolds.

Related

• The Penrose transform in quaternionic geometry
• On tame ρ-quaternionic manifolds
• Quaternionic-like manifolds and homogeneous twistor spaces
• Twistorial structures revisited
• Projective structures and ρ-connections