Abstract
We will investigate geodesics in 2-step Carnot groups. And, by applying this, we will prove that every isometry of 2-step Carnot group $N$ fixing the identity is an automorphism of Lie group $N$. Our argument will be elementary.
Finally, we will see that the same conclusion holds for general Carnot groups.
Citation
Iwao Kishimoto. "Geodesics and isometries of Carnot groups." J. Math. Kyoto Univ. 43 (3) 509 - 522, 2003. https://doi.org/10.1215/kjm/1250283693
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