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arXiv · 2610.03305

Sub-Riemannian geodesics in the affine-additive group

Elia Bubani·Ioannis D. Platis·Georgios I. Simantiras·Dimitrios Tsolis
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Abstract

We derive the sub-Riemannian geodesics of the affine-additive group using the Pontryagin Maximum Principle (PMP) and compute the associated cut times. We then proceed to construct the Carnot-Carathéodory sphere of the affine-additive group as well as the flask surface; the latter is the analogue of the Pansu sphere (bubble set) in the first Heisenberg group.

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Elia Bubani, Ioannis D. Platis, Georgios I. Simantiras, Dimitrios Tsolis. 2026-10-02. Sub-Riemannian geodesics in the affine-additive group. https://arxiv.org/abs/2610.03305

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