Non-singular geodesic orbit nilmanifolds
Differential Geometry
2025-04-23 v2 Geometric Topology
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.
Cite
@article{arxiv.2504.12391,
title = {Non-singular geodesic orbit nilmanifolds},
author = {Yuri Nikolayevsky and Wolfgang Ziller},
journal= {arXiv preprint arXiv:2504.12391},
year = {2025}
}