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arXiv · 2511.01890

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

Jiro Adachi
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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.

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Jiro Adachi. 2025-10-26. Existence and classification of the Cartan $(2,3,5)$-distribution. https://arxiv.org/abs/2511.01890

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