Characterisation of the sub-Riemannian isometry groups of the H-type groups
Characterisation of the sub-Riemannian isometry groups of the H-type groups
复制标题
DOI：
10.1017/s000497270003584x
复制
发表时间：
2004-08
影响因子：
0.7
通讯作者：
Kanghai Tan;Xiao-Ping Yang
中科院分区：
文献类型：
--
作者：
Kanghai Tan;Xiao-Ping Yang
对于H-型群G，我们首先给出它的最短子黎曼测地线的显式方程。我们利用G中次黎曼测地线的性质来刻画等距群ISO（G）关于Carnot-Carathéodory度量.证明ISO（G）与G的标准黎曼度量的等距群重合。
For a H-type group G, we first give explicit equations for its shortest sub-Riemannian geodesics. We use properties of sub-Riemannian geodesics in G to characterise the isometry group ISO(G) with respect to the Carnot-Carathéodory metric. It turns out that ISO(G) coincides with the isometry group with respect to the standard Riemannian metric of G.