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arXiv · 2406.11509

Reductions of path structures and classification of homogeneous structures in dimension three

Elisha Falbel·Martin Mion-Mouton·Jose M. Veloso
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Abstract

In this paper we show that if a path structure has non-vanishing curvature at a point then it has a canonical reduction to a Z/2Z-structure at a neighbourhood of that point (in many cases it has a canonical parallelism). A simple implication of this result is that the automorphism group of a non-flat path structure is of maximal dimension three (a result by Tresse of 1896). We also classify the invariant path structures on three-dimensional Lie groups.

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Elisha Falbel, Martin Mion-Mouton, Jose M. Veloso. 2024-06-17. Reductions of path structures and classification of homogeneous structures in dimension three. https://arxiv.org/abs/2406.11509

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