We apply the notions of Gaussian curvature and mean curvature to rotation surfaces in sub-Riemannian Heisenberg space H1\documentclass[12pt]{minimal}
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\begin{document}$$\mathbb H^1$$\end{document}. In Diniz and Veloso (J Dyn Control Syst 22(4):807–820, 2016) we introduced a notion of Gaussian curvature, and here we classify rotation surfaces which are of constant Gaussian curvature. We study these surfaces rotating a horizontal curve γ\documentclass[12pt]{minimal}
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\begin{document}$$\gamma $$\end{document} around the z-axis. They have a resemblance to rotation surfaces of constant curvature in Euclidean space R3\documentclass[12pt]{minimal}
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\begin{document}$$\mathbb R^3$$\end{document}. The rotation surfaces of constant mean curvature in H1\documentclass[12pt]{minimal}
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\begin{document}$$\mathbb H^1$$\end{document} are well known. The mean curvature of a rotation surface S in H1\documentclass[12pt]{minimal}
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\begin{document}$$\mathbb H^1$$\end{document} is the curvature of the curve in R2\documentclass[12pt]{minimal}
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\begin{document}$$\mathbb R^2$$\end{document} which is the projection of γ\documentclass[12pt]{minimal}
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\begin{document}$$\gamma $$\end{document}, and we use this property to classify them.
