The gap phenomenon in the dimension study of finite type systems

Abstract

In this paper several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the symmetries of geometric structures and differential equations. A general result clarifying this effect in the case, when the structure is associated to a vector distribution, is proposed.

The complete description of the structure of equivalence classes of rank 2 distributions with 7-dimensional symmetry algebra (enhancing the one of Cartan) is added in section 5

References in corpus (2)

• Two-dimensional superintegrable metrics with one linear and one cubic integral
• Symmetries of almost complex structures and pseudoholomorphic foliations

Cited by in corpus (1)

• Nearly Kähler Geometry and $(2,3,5)$-Distributions via Projective Holonomy