On Sub-Riemannian and Riemannian Structures on the Heisenberg Groups

被引：5

作者：

Biggs, Rory ^{[1
]}

Nagy, Peter T. ^{[2
]}

机构：

[1] Rhodes Univ, Dept Math Pure & Appl, POB 94, ZA-6140 Grahamstown, South Africa

[2] Obuda Univ, Inst Appl Math, Becsi Ut 96-B, H-1034 Budapest, Hungary

来源：

JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS | 2016年 / 22卷 / 03期

关键词：

Sub-Riemannian geometry; Riemannian geometry; Heisenberg group; Isometries; Geodesics; Totally geodesic subgroups; Conjugate locus; 2-STEP NILPOTENT GROUPS; LEFT INVARIANT METRICS; HOMOGENEOUS NILMANIFOLDS; GEODESICS; GEOMETRY; CURVATURES; MOTIONS; SPACES;

D O I：

10.1007/s10883-016-9316-9

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We consider the left-invariant sub-Riemannian and Riemannian structures on the Heisenberg groups. A classification of these structures was found previously. In the present paper, we find (for each normalized structure) the isometry group, the exponential map, the totally geodesic subgroups, and the conjugate locus. Finally, we determine the minimizing geodesics from identity to any given endpoint. (Several of these points have been covered, to varying degrees, by other authors.).

引用

页码：563 / 594

页数：32

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