The gap phenomenon in the dimension study of finite type systems

2011/11/27 by Boris Kruglikov, Kruglikov, Boris
Mathematics · #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.CA #math.DG

paper · pdf · doi:10.48550/arxiv.1111.6315

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

openalex publication_date 2011/11/27 · arxiv created 2012/03/04 · arxiv updated 2012/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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