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arXiv · 2504.12391

Non-singular geodesic orbit nilmanifolds

Yuri Nikolayevsky·Wolfgang Ziller
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Abstract

A Riemannian manifold is called a geodesic orbit manifolds, GO for short, if any geodesic is an orbit of a one-parameter group of isometries. By a result of C.Gordon, a non-flat GO nilmanifold is necessarily a two-step nilpotent Lie group with a left-invariant metric. We give a complete classification of non-singular GO nilmanifolds. Besides previously known examples, there are new families with 3-dimensional center, and two one-parameter families of dimensions 14 and 15.

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Yuri Nikolayevsky, Wolfgang Ziller. 2025-04-16. Non-singular geodesic orbit nilmanifolds. https://arxiv.org/abs/2504.12391

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