Cone structures and path geometries with constant torsion
Differential Geometry
2025-08-15 v1
Abstract
We study three-dimensional path geometries with nontrivial torsion of maximal rank. We introduce the notion of constant torsion and show that such path geometries are in one-to-one correspondence with certain cone structures modeled on homogeneous ruled surfaces. We also describe these cone structures in terms of solutions to new integrable systems admitting dispersionless, non-isospectral Lax pairs.
Cite
@article{arxiv.2508.10564,
title = {Cone structures and path geometries with constant torsion},
author = {Wojciech Kryński},
journal= {arXiv preprint arXiv:2508.10564},
year = {2025}
}