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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{bubani2026subriemannian,
  title = {{Sub-Riemannian geodesics in the affine-additive group}},
  author = {Elia Bubani and Ioannis D. Platis and Georgios I. Simantiras and Dimitrios Tsolis},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03305},
  eprint = {2610.03305},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03305},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Sub-Riemannian geodesics in the affine-additive group
AU  - Elia Bubani
AU  - Ioannis D. Platis
AU  - Georgios I. Simantiras
AU  - Dimitrios Tsolis
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.03305
UR  - https://arxiv.org/abs/2610.03305
AB  - 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.
ER  -