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arXiv · 2508.10564

Cone structures and path geometries with constant torsion

Wojciech Kryński
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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.

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Wojciech Kryński. 2025-08-14. Cone structures and path geometries with constant torsion. https://arxiv.org/abs/2508.10564

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