2006/10/23 by E. Loubeau, Eric Loubeau, Loubeau, Eric +2
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Primary 53C43 #Secondary 53C28 #math.DG #msc:53C28 #msc:53C43
paper · pdf · doi:10.48550/arxiv.math/0610676
minor corrections
openalex publication_date 2006/10/23 · arxiv created 2007/06/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define, on smooth manifolds, the notions of almost twistorial structure and twistorial map, thus providing a unified framework for all known examples of twistor spaces. The condition of being harmonic morphisms naturally appears among the geometric properties of submersive twistorial maps between low-dimensional Weyl spaces endowed with a nonintegrable almost twistorial structure due to Eells and Salamon. This leads to the twistorial characterisation of harmonic morphisms between Weyl spaces of dimensions four and three. Also, we give a thorough description of the twistorial maps with one-dimensional fibres from four-dimensional Weyl spaces endowed with the almost twistorial structure of Eells and Salamon.