What question did this study set out to answer?

The aim is to classify non-singular geodesic orbit nilmanifolds, expanding on known examples.

February 12, 2026Open Access

Non-singular geodesic orbit nilmanifolds

Key Points

The aim is to classify non-singular geodesic orbit nilmanifolds, expanding on known examples.
Defined the properties of geodesic orbit manifolds.
Utilized results from C. Gordon regarding nilmanifolds.
Introduced new families with specific dimensional centers.
Identified new families of non-singular GO nilmanifolds with 3-dimensional centers.
Described two one-parameter families of dimensions 14 and 15.
Confirmed that non-flat GO nilmanifolds are two-step nilpotent Lie groups.

Abstract

Abstract 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.

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Cite This Study

Nikolayevsky et al. (Tue,) studied this question.

synapsesocial.com/papers/698d6e055be6419ac0d535da https://doi.org/https://doi.org/10.1007/s10231-026-01661-9

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