2005/12/27 by Jaroslav Hrdina, Hrdina, Jaroslav, Jan Slovák +2
Mathematics · Physics and Astronomy · #53C15 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #math.DG #msc:53C15
paper · pdf · doi:10.48550/arxiv.math/0512593
arxiv created 2005/12/27 · openalex publication_date 2005/12/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by the analogies between the projective and the almost quaternionic geometries, we study the generalized planar curves and mappings. We follow, recover, and extend the classical approach as developed by Mikes and Sinyukov. Then we exploit the impact of the general results in the almost quaternionic geometry. In particular we show, that the natural class of H--planar curves coincides with the class of all geodesics of the so called Weyl connections and preserving this class turns out to be the necessary and sufficient condition on diffeomorphisms to become morphisms of almost quaternionic geometries.