Article Dans Une Revue (Article De Synthèse) Transformation Groups Année : 2025

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

Résumé

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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hal-04612815 , version 1 (14-06-2024)

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Elisha Falbel, Martin Mion-Mouton, Jose Miguel Veloso. Reductions of path structures and classification of homogeneous structures in dimension three. Transformation Groups, 2025, ⟨10.1007/s00031-025-09937-9⟩. ⟨hal-04612815⟩
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