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Pré-Publication, Document De Travail Année : 2024

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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  • HAL Id : hal-04612815 , version 1

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Elisha Falbel, Martin Mion-Mouton, Jose M. Veloso. Reductions of path structures and classification of homogeneous structures in dimension three. 2024. ⟨hal-04612815⟩
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