Existence and classification of the Cartan $(2,3,5)$-distribution

Jiro Adachi

Existence and classification of the Cartan $(2,3,5)$-distribution

Differential Geometry 2025-11-05 v1 Geometric Topology

Authors: Jiro Adachi

Abstract

The Cartan $(2,3,5)$ -distribution is a tangent distribution of rank~ $2$ on a $5$ -dimensional manifold satisfying certain generic conditions. The necessary and sufficient condition for a manifold to admit such a structure is established in this paper. The condition obtained is purely topological. In addition, the classification of such structures, up to homotopy as formal Cartan distributions, is obtained.

Keywords

Cartan distribution rank-2 distribution topological condition classification manifold

Cite

@article{arxiv.2511.01890,
  title  = {Existence and classification of the Cartan $(2,3,5)$-distribution},
  author = {Jiro Adachi},
  journal= {arXiv preprint arXiv:2511.01890},
  year   = {2025}
}

Comments

36 pages, 4 figures

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