Singularities of tangent surfaces in Cartan's split \(G_2\)-geometry (Q281842)

In this paper, the authors study the correspondence between the Cartan distribution and the contact distribution with Monge structure on spaces of five variables in the split \(G_2\)-geometry. They give a generic classification of singularities of tangent surfaces to Cartan curves and to Monge curves via a viewpoint of duality of singularities. The paper completes the classification of generic singularities of simple Lie algebras of rank 2.