Abnormal extremals of left-invariant sub-Finsler quasimetrics on four-dimensional Lie groups with three-dimensional generating distributions

2021/11/04 by Berestovskii, Valera, И. А. Зубарева, Zubareva, Irina
Physics and Astronomy · Mathematics · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2111.02988

Abstract

We find three-dimensional subspaces of four-dimensional connected Lie algebras, generating these algebras, and abnormal extremals on connected Lie groups with these Lie algebras and with left-invariant sub-Finsler quasimetrics defined by seminorms on such subspaces. In terms of the structure constants of Lie algebras and dual seminorms, we establish a criterion for the strong abnormality of these extremals.

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