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arXiv · 2603.08330

Horizontal curvatures of surfaces in 3D contact sub-Riemannian Lie groups

Elia Bubani·Andrea Pinamonti·Ioannis D. Platis·Dimitrios Tsolis
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Abstract

In this paper we study horizontal curvatures for surfaces embedded in three-dimensional contact sub-Riemannian Lie groups. Using a Riemannian approximation scheme, we derive explicit formulas for horizontal Gauss curvature, horizontal mean curvature, and symplectic distortion for surfaces embedded in three dimensional Lie groups with a sub-Riemannian structure obtained by a contact form. We focus on two primary examples: the Heisenberg group and the affine-additive group. We classify surfaces of revolution within these groups that exhibit constant horizontal curvatures, often expressing their profiles through elementary or elliptic integrals.

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Elia Bubani, Andrea Pinamonti, Ioannis D. Platis, Dimitrios Tsolis. 2026-03-09. Horizontal curvatures of surfaces in 3D contact sub-Riemannian Lie groups. https://arxiv.org/abs/2603.08330

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