2011/04/12 by Roger Bielawski, Bielawski, Roger, Lorenz Schwachhöfer +1
Mathematics · Physics and Astronomy · #14F05 #14H60 #32L25 #53C26 #53C28 #81E13 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #Geometry and complex manifolds #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.1104.2270
openalex publication_date 2011/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by strong desire to understand the natural geometry of moduli spaces of hyperbolic monopoles, we introduce and study a new type of geometry: pluricomplex geometry. It is a generalisation of hypercomplex geometry: we still have a 2-sphere of complex structures, but they no longer behave like unit imaginary quaternions. We still require, however, that the 2-sphere of complex structures determines a decomposition of the complexified tangent space as tensor product of C2n and C2. Among interesting properties of pluricomplex manifold is the existence of a canonical torsion free connection. Pluricomplex manifolds have also remarkable twistor theory: they parameterise algebraic curves of higher genera.