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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
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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.
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- Copyright © Australian Mathematical Society 2004
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