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Abnormal Extremals of Left-Invariant Sub-Finsler Quasimetrics on Four-Dimensional Lie Groups
Siberian Mathematical Journal ( IF 0.5 ) Pub Date : 2021-05-27 , DOI: 10.1134/s0037446621030010
V. N. Berestovskii , I. A. Zubareva

We find the abnormal extremals on four-dimensional connected Lie groups with left-invariant sub-Finsler quasimetric defined by a seminorm on a two-dimensional subspace of the Lie algebra generating the algebra. In terms of the structure constants of a Lie algebra and the Minkowski support function of the unit ball of the seminorm on the two-dimensional subspace of a Lie algebra which defines a quasimetric, we establish a criterion for the strict abnormality of these extremals.



中文翻译:

四维李群上左不变子芬斯勒拟度量的异常极值

我们在生成代数的李代数的二维子空间上的半范数定义了具有左不变子芬斯勒拟度量的四维连通李群上的异常极值。根据李代数的结构常数和定义拟度量的李代数二维子空间上半范数单位球的闵可夫斯基支持函数,我们建立了这些极值的严格异常的判据。

更新日期:2021-05-28
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