Explicit Formulae for Geodesics in Left-Invariant Sub-Finsler Problems on Heisenberg Groups via Convex Trigonometry

被引：3

作者：

Lokutsievskiy, L. V. ^{[1
]}

机构：

[1] Russian Acad Sci, Steklov Math Inst, Moscow, Russia

来源：

JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS | 2021年 / 27卷 / 04期

基金：

俄罗斯科学基金会;

关键词：

Convex trigonometry; Sub-Finsler geodesics Heisenberg groups; Shelupsky functions;

D O I：

10.1007/s10883-020-09516-z

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In the present paper, we obtain explicit formulae for geodesics in some left-invariant sub-Finsler problems on Heisenberg groups H2n+1. Our main assumption is the following: the compact convex set of unit velocities at identity admits a generalization of spherical coordinates. This includes convex hulls and sums of coordinate 2-dimensional sets, all left-invariant sub-Riemannian structures on H2n+1, and unit balls in L-p-metric for 1 <= p <= infinity. In the last case, extremals are obtained in terms of incomplete Euler integral of the first kind.

引用

页码：661 / 681

页数：21