Sub-Riemannian Geodesics on the Multidimensional Heisenberg Group

被引：0
|
作者：
Panzhenskii V.I. [1 ]
Surina O.P. [1 ]
机构：
[1] Penza State University, Penza
来源：
Journal of Mathematical Sciences | 2023年 / 276卷 / 4期
关键词：
53B21; geodesic line; Heisenberg group; left-invariant contact metric structure; sub-Riemannian structure;
D O I：
10.1007/s10958-023-06776-5
中图分类号：
学科分类号：
摘要：
In this paper, we study the structure of truncated connections on the multidimensional Heisenberg group endowed with a left-invariant sub-Riemannian structure. We find that sub-Riemannian geodesic lines are parabolas whose orthogonal projections onto the corresponding contact planes are straight lines. In addition to such parabolas, some straight lines lying in contact planes are also geodesics. © 2023, Springer Nature Switzerland AG.
引用
收藏
页码：541 / 551
页数：10
相关论文
共 50 条
  • [1] Homogeneous Sub-Riemannian Geodesics on a Group of Motions of the Plane
    Yu. L. Sachkov
    [J]. Differential Equations, 2021, 57 : 1550 - 1554
  • [2] Geodesics in the sub-Riemannian problem on the group SO(3)
    Beschastnyi, I. Yu.
    Sachkov, Yu. L.
    [J]. SBORNIK MATHEMATICS, 2016, 207 (07) : 915 - 941
  • [3] An Extrinsic Approach to Sub-Riemannian Geodesics on the Orthogonal Group
    Huper, Knut
    Markina, Irina
    Leite, Fatima Silva
    [J]. CONTROLO 2020, 2021, 695 : 274 - 283
  • [4] Homogeneous Sub-Riemannian Geodesics on a Group of Motions of the Plane
    Sachkov, Yu L.
    [J]. DIFFERENTIAL EQUATIONS, 2021, 57 (11) : 1550 - 1554
  • [5] ON THE SHORTEST SUB-RIEMANNIAN GEODESICS
    PETROV, NN
    [J]. DIFFERENTIAL EQUATIONS, 1994, 30 (05) : 705 - 711
  • [6] SUB-RIEMANNIAN GEODESICS ASSOCIATED TO CR-GEOMETRY ON HEISENBERG GROUP H3
    Frolik, Stanislav
    Hrdina, Jaroslav
    [J]. UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, 2023, 85 (04): : 55 - 66
  • [7] Riemannian and sub-Riemannian structures on a cotangent bundle of Heisenberg group
    Sukilovic, Tijana
    Vukmirovic, Srdjan
    [J]. FILOMAT, 2023, 37 (25) : 8481 - 8488
  • [8] Quantum Computational Riemannian and Sub-Riemannian Geodesics
    Shizume, Kosuke
    Nakajima, Takao
    Nakayama, Ryo
    Takahashi, Yutaka
    [J]. PROGRESS OF THEORETICAL PHYSICS, 2012, 127 (06): : 997 - 1008
  • [9] An Introduction to the Heisenberg Group and the sub-Riemannian Isoperimetric Problem
    Beltita, Daniel
    [J]. REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES, 2009, 54 (01): : 74 - 75
  • [10] An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem
    Varga, Csaba
    [J]. STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, 2008, 53 (04): : 126 - 127
12345