Igor Zelenko

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math.DG2026

$G_{2}$ and the Maximally Symmetric (3, 8) Distribution with 6-Dimensional Square

Nicklas Day, Boris Doubrov, Igor Zelenko

In 1910, Ãlie Cartan famously realized the split real form of the exceptional Lie group $G_{2}$ as the symmetry group of the maximally symmetric rank 2 distribution on a 5-dimension…

math.DG2026

Generalized pseudo-product structures and finite type distributions via abnormal extremals

Boris Doubrov, Igor Zelenko

We generalize the classical Tanaka result on the finiteness of symmetry algebra for non-degenerate pseudo-product structures to the case when the completely-integrable distribution…

math.DG2026

Canonical Frames for Bracket Generating Rank 2 Distributions which are not Goursat

Nicklas Day, Igor Zelenko

We complete a uniform construction of canonical absolute parallelism for bracket generating rank $2$ distributions with $5$ -dimensional cube on $n$ -dimensional manifold with $n\geq…

math.DG2025

Symplectification of Rank 2 Distributions, Normal Cartan Connections, and Cartan Prolongations

Nicklas Day, Boris Doubrov, Igor Zelenko

We study the Doubrov--Zelenko symplectification procedure for rank $2$ distributions with $5$ -dimensional cube -- originally motivated by optimal control theory -- through the lens…

G2​ and the Maximally Symmetric (3, 8) Distribution with 6-Dimensional Square

Generalized pseudo-product structures and finite type distributions via abnormal extremals

Canonical Frames for Bracket Generating Rank 2 Distributions which are not Goursat

Symplectification of Rank 2 Distributions, Normal Cartan Connections, and Cartan Prolongations

$G_{2}$ and the Maximally Symmetric (3, 8) Distribution with 6-Dimensional Square