Singular curves of hyperbolic $(4, 7)$-distributions of type $C_3$

Author:

Goo Ishikawa, Yoshinori Machida

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), Representation Theory (math.RT)

journal:

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date:

2023-10-27 16:00:00

Abstract

A distribution of rank $4$ on a $7$-dimensional manifold is called a $(4, 7)$-distribution if its local sections generate the whole tangent space by taking Lie brackets once. Singular curves of $(4, 7)$-distributions are studied in this paper. In particular the class of hyperbolic $(4, 7)$-distributions of type $C_3$ is introduced and singular curves are completely described via prolongations for them.