Sub-Riemannian geodesics in the affine-additive group
arXiv:2610.03305
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.
30 pages, 9 figures, comments are welcome!