Symmetries of (2,3,5)-distributions and associated Legendrian cone structures

2024/08/21 by Jun-Muk Hwang, Hwang, Jun-Muk, Dennis The +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #34C41 #53A55 #58J70 #Advanced Statistical Methods and Models #Differential Geometry (math.DG) #FOS: Mathematics #Financial Risk and Volatility Modeling #Primary: 58A30 #Secondary: 32L25 #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2408.11459

openalex publication_date 2024/08/21 · openalex created_date 2024/12/16 · openalex updated_date 2026/07/28

Abstract

We exploit a natural correspondence between holomorphic (2,3,5)-distributions and nondegenerate lines on holomorphic contact manifolds of dimension 5 to present a new perspective in the study of symmetries of (2,3,5)-distributions. This leads to a number of new results in this classical subject, including an unexpected relation between the multiply-transitive families of models having 7- and 6-dimensional symmetries, and a one-to-one correspondence between equivalence classes of nontransitive (2,3,5)-distributions with 6-dimensional symmetries and nonhomogeneous nondegenerate Legendrian curves in ℙ³. An ingredient for establishing the former is an explicit classification of homogeneous nondegenerate Legendrian curves in ℙ³, which we present.

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