Hyperbolic Twistor Spaces

2003/12/18 by D. E. Blair, David E. Blair, Blair, D. E. +6 · 2 citations
Mathematics · #32L25 #53C28 #53c26 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematics and Applications #math.DG #msc:32L25 #msc:53C28 #msc:53c26

paper · pdf · doi:10.48550/arxiv.math/0312364

LaTeX, 22 pages, to appear in Rocky Mountain J.Math

arxiv created 2003/12/18 · openalex publication_date 2003/12/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In contrast to the classical twistor spaces whose fibres are 2-spheres, we introduce twistor spaces over manifolds with almost quaternionic structures of the second kind in the sense of P. Libermann whose fibres are hyperbolic planes. We discuss two natural almost complex structures on such a twistor space and their holomorphic functions.

Cited by

• The twistor lifts of surfaces in 4-spaces
• The equations of Gauss, Codazzi and Ricci of surfaces in 4-dimensional space forms

Related

• Twistor Spaces of Riemannian Manifolds with Even Clifford Structures
• Twistor space of a generalized quaternionic manifold
• On a class of twistorial maps
• Harmonic morphisms between Weyl spaces and twistorial maps II
• Twistors of Almost Quaternionic Manifolds