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<p>A Riemannian manifold is called a <i>geodesic orbit</i> manifold, 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.</p>

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Non-singular geodesic orbit nilmanifolds

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月10日

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  • Y. Nikolayevsky,
  • W. Ziller

摘要

A Riemannian manifold is called a geodesic orbit manifold, 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.