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PreprintCC BY 4.0arXiv

On the Structure of Sub-Riemannian Geodesic Orbit Manifolds

  • Huihui An
  • Zaili Yan
  • Hui Zhang
  • Shaoxiang Zhang
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Abstract

We study homogeneous sub-Riemannian manifolds whose normal extremals are orbits of one-parameter subgroups of the acting group. Our first main result shows that every sub-Riemannian geodesic orbit manifold satisfies the Goh condition and consequently admits no strictly abnormal length minimizers. Our second main result classifies all compact, connected, simply connected sub-Riemannian geodesic orbit manifolds with nonabelian simple isotropy group, thereby extending the Riemannian classification of Chen, Nikolayevsky and Nikonorov.

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Cite

BibTeXRIS
BibTeX
@misc{an2026structure,
  title = {{On the Structure of Sub-Riemannian Geodesic Orbit Manifolds}},
  author = {Huihui An and Zaili Yan and Hui Zhang and Shaoxiang Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11292},
  eprint = {2610.11292},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.11292},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the Structure of Sub-Riemannian Geodesic Orbit Manifolds
AU  - Huihui An
AU  - Zaili Yan
AU  - Hui Zhang
AU  - Shaoxiang Zhang
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.11292
UR  - https://arxiv.org/abs/2610.11292
AB  - We study homogeneous sub-Riemannian manifolds whose normal extremals are orbits of one-parameter subgroups of the acting group. Our first main result shows that every sub-Riemannian geodesic orbit manifold satisfies the Goh condition and consequently admits no strictly abnormal length minimizers. Our second main result classifies all compact, connected, simply connected sub-Riemannian geodesic orbit manifolds with nonabelian simple isotropy group, thereby extending the Riemannian classification of Chen, Nikolayevsky and Nikonorov.
ER  -