Parallel (co-)tractors and the geometry of first BGG solutions on almost Grassmannian structures
Differential Geometry
2026-05-06 v2
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.
Keywords
Cite
@article{arxiv.2507.17605,
title = {Parallel (co-)tractors and the geometry of first BGG solutions on almost Grassmannian structures},
author = {Zhangwen Guo},
journal= {arXiv preprint arXiv:2507.17605},
year = {2026}
}
Comments
21 pages. Revised version incorporating the referee's report