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arXiv · 2610.11292

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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Huihui An, Zaili Yan, Hui Zhang, Shaoxiang Zhang. 2026-10-08. On the Structure of Sub-Riemannian Geodesic Orbit Manifolds. https://arxiv.org/abs/2610.11292

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