Work

Prolongation of $(8,15)$-Distribution of Type $F_4$ by Singular Curves

Year: 2025

Type: article

Abstract: Cartan gives the model of $(8, 15)$-distribution with the exceptional simple Lie algebra $F_4$ as its symmetry algebra in his paper (1893), which is published one year before his thesis. In the present paper, we study abnormal extremals (singular curves) of Cartan's model from viewpoints of sub-Riemannian geometry and geometric control theory.Then we construct the prolongation of Cartan's model based on the data related to its singular curves, and obtain the nilpotent graded Lie algebra which is isomorphic to the negative part of the graded Lie algebra $F_4$.

Source: Symmetry Integrability and Geometry Methods and Applications

DOI: 10.3842/sigma.2025.076

Authors: Goo Ishikawa, Yoshinori Machida

Institutions: Hokkaido University, Shizuoka University, University of Shizuoka

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

Funders: Japan Society for the Promotion of Science, Research Institute for Mathematical Sciences, Division of Mathematical Sciences, Core Research for Evolutional Science and Technology

Awards: Development of geometric singularity theory and its applications, G6718509927