The sub-Riemannian cut locus of H-type groups

被引：4

作者：

Autenried, Christian ^{[1
]}

Godoy Molina, Mauricio ^{[1
,2
]}

机构：

[1] Univ Bergen, Dept Math, POB 7803, NO-5020 Bergen, Norway

[2] Univ La Frontera, Dept Matemat & Estad, Ave Francisco Salazer 01145,Casilla 54-D, Temuco, Chile

来源：

MATHEMATISCHE NACHRICHTEN | 2016年 / 289卷 / 01期

关键词：

Sub-Riemannian geodesics; H-type group; cut locus; HEAT KERNEL;

D O I：

10.1002/mana.201400368

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the present paper we prove that the sub-Riemannian cut locus at the origin of a wide class of nilpotent groups of step two, called H-type groups, corresponds to the center of the group. We obtain this result by completely describing the sub-Riemannian geodesics in the group, and using these to obtain three disjoint sets of points in the group determined by the number of geodesics joining them to the origin. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：4 / 12

页数：9

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