Abnormal extremals of left-invariant sub-Finsler quasimetrics on\n four-dimensional Lie groups

2020/11/08 by Berestovskii, Valera, И. А. Зубарева, Zubareva, Irina
Engineering · Medicine · Physics and Astronomy · #49J15 #53C17 #53C22 #53C60 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Material Science and Thermodynamics #Medical and Biological Sciences

paper · pdf · doi:10.48550/arxiv.2011.03940

openalex publication_date 2020/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Abnormal extremals on four-dimensional connected Lie groups with\nleft-invariant sub-Finsler quasimetric, defined by a seminorm on a\ntwo-dimensional subspace of the Lie algebra generating the algebra, are found.\nIn terms of structure constant of Lie algebra and supporting Minkowski function\nfor the unit ball of seminorm on two-dimensional subspace of Lie algebra,\ndefining a quasimetric, we establish a criterion for strict abnormality of\nthese extremals.\n

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