Infinite Geodesics of Sub-Finsler Distances in Heisenberg Groups

被引：0

作者：

Balogh, Zoltan M. ^{[1
]}

Calogero, Andrea ^{[2
]}

机构：

[1] Univ Bern, Dept Math & Stat, Sidlerstr 5, CH-3012 Bern, Switzerland

[2] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, Via Cozzi 53, I-20125 Milan, Italy

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2021年 / 2021卷 / 07期

基金：

瑞士国家科学基金会;

关键词：

TIME;

D O I：

10.1093/imrn/rnz074

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider Heisenberg groups equipped with a sub-Finsler metric. Using methods of optimal control theory we prove that in this geometric setting the infinite geodesics are horizontal lines under the assumption that the sub-Finsler metric is defined by a strictly convex norm. This answers a question posed in [8] and has applications in the characterization of isometric embeddings into Heisenberg groups.

引用

页码：4805 / 4837

页数：33

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