Two Fefferman-type constructions involving almost Grassmann structures and path geometries

2025/09/05 by Zhangwen Guo, Guo, Zhangwen
Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2509.04878

openalex publication_date 2025/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We introduce a Fefferman-type construction that associates an almost Grassmannian structure of type (2,n+1) to every (n+1)-dimensional path geometry. We prove that the construction is normal and provide two equivalent characterizing conditions for all almost Grassmannian structures which locally arise from this construction: one in terms of certain parallel tractors and the other in terms of a Weyl connection of an almost Grassmann structure. We prove that the latter condition is independent of the choice of Weyl connection. We then introduce a related Fefferman-type construction associating an almost Grassmannian structure of type (2,n+1) to every almost Grassmannian structure of type (2,n). We prove that this construction is non-normal and characterize all almost Grassmannian structures which locally arise in this way in Cartan geometric terms.

Citations

• Parallel (co-)tractors and the geometry of first BGG solutions on almost Grassmannian structures
• On quaternionic contact Fefferman spaces
• Free n-distributions: holonomy, sub-Riemannian structures, Fefferman constructions and dual distributions
• Correspondence spaces and twistor spaces for parabolic geometries

Related

• Conformal and Grassmann structures
• Parallel (co-)tractors and the geometry of first BGG solutions on almost Grassmannian structures
• On the theory of almost Grassmann structures
• Dyck paths, binary words, and Grassmannian permutations avoiding an increasing pattern
• Interactions between para-quaternionic and Grassmannian geometry