Parallel (co-)tractors and the geometry of first BGG solutions on almost Grassmannian structures

2025/07/23 by Zhangwen Guo, Guo, Zhangwen · 1 citation
Engineering · Mathematics · #Advanced Differential Equations and Dynamical Systems #Control and Dynamics of Mobile Robots #Differential Geometry (math.DG) #FOS: Mathematics #Vehicle Dynamics and Control Systems

paper · pdf · doi:10.48550/arxiv.2507.17605

openalex publication_date 2025/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We study the standard tractor bundle and the standard cotractor bundle of an almost Grassmann structure: We provide explicit formulae for their splitting operators, first BGG operators as well as prolongation connections. We characterize parallel tractors and cotractors as well as the solutions of the BGG operators in standard geometric terms. Moreover, we describe the geometry canonically endowed on the zero locus of a solution of the first BGG operators.

Citations

• Geometry of solutions to the c-projective metrizability equation
• Metrics in projective differential geometry: the geometry of solutions\n to the metrizability equation
• On a new normalization for tractor covariant derivatives
• Bernstein-Gelfand-Gelfand sequences

Cited by

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

Related

• Two Fefferman-type constructions involving almost Grassmann structures and path geometries
• Projective Geometry I: Principles and Properties
• Almost Parallel Structures
• Conformal and Grassmann structures
• On the GIT quotient of Grassmannians by one dimensional torus