Work

On the Structure of Sub-Riemannian Geodesic Orbit Manifolds

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.11292

Authors: An, Huihui, Yan, Zaili, Zhang, Hui, Zhang, Shaoxiang

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7221164927

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