2005/11/27 by Stefan Ivanov, Ivan Minchev, Ivanov, Stefan +3
Mathematics · Physics and Astronomy · #5350 #53C15 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #hep-th #math-ph #math.DG #math.MP #msc:5350 #msc:53C15
paper · pdf · doi:10.48550/arxiv.math/0511657
LaTeX, 16 pages, no figures
arxiv created 2005/11/27 · openalex publication_date 2005/11/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the integrability of natural almost complex structures on the twistor space of an almost para-quaternionic manifold as well as the integrability of natural almost paracomplex structures on the reflector space of an almost para-quaternionic manifold constructed with the help of a para-quaternionic connection. We show that if there is an integrable structure it is independent on the para-quaternionic connection. In dimension four, we express the anti-self-duality condition in terms of the Riemannian Ricci forms with respect to the associated para-quaternionic structure.