2021/03/02 by Guangzhen Ren, Wei Wang, Ren, Guangzhen +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG
paper · pdf · doi:10.48550/arxiv.2103.01549
22 pages
arxiv created 2021/03/02 · openalex publication_date 2021/03/02 · arxiv updated 2021/03/03 · openalex created_date 2021/03/15 · openalex updated_date 2026/07/28
In this paper, we introduce notions of α-planes in 5D complex Heisenberg group and the twistor space as the moduli space of all α-planes. So we can define an anti-self-dual (ASD) connection as a connection flat over all α-planes. This geometric approach allows us to establish Penrose-Ward correspondence between ASD connections over 5D complex Heisenberg group and a class of holomorphic vector bundles on the twistor space. By Atiyah-Ward ansätz, we also construct a family of ASD connections on 5D complex Heisenberg group. When restricted to 5D real Heisenberg group, the flat model of 5D contact manifolds, an ASD connection satisfies the horizontal part of the contact instanton equation introduced by physicists.