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Characterisation of the sub-Riemannian isometry groups of the H-type groups

Published online by Cambridge University Press:  17 April 2009

Kang-Hai Tan  and
Xiao-Ping Yang
Kang-Hai Tan
Affiliation:
Department of Applied Mathematics, Science School Nanjing University of Science and Technology, 210094, Nanjing, Peoples Republic China, e-mail: tankanghai2000@yahoo.com.cn, yangxp@mail.njust.edu.cn
Xiao-Ping Yang
Affiliation:
Department of Applied Mathematics, Science School Nanjing University of Science and Technology, 210094, Nanjing, Peoples Republic China, e-mail: tankanghai2000@yahoo.com.cn, yangxp@mail.njust.edu.cn
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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.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 70 , Issue 1 , August 2004 , pp. 87 - 100
Copyright
Copyright © Australian Mathematical Society 2004

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