The gap phenomenon in the dimension study of finite type systems

TL;DR

This paper investigates the gap phenomenon in the dimensions of symmetric models related to geometric structures, providing examples and a general result for structures associated with vector distributions.

Contribution

It introduces new examples of gap phenomena and proposes a general result for structures linked to vector distributions.

Findings

Examples of gaps between maximal and submaximal symmetric models

Analysis of integrals and symmetries in geometric structures

A general result clarifying the gap phenomenon for vector distributions

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.