Non-singular geodesic orbit nilmanifolds
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.
Fields of Study & Subjects
Advanced Differential Geometry Research
Geometric Analysis and Curvature Flows
Geometry and complex manifolds
Publication details
- Journal / source
- Annali di Matematica Pura ed Applicata (1923 -)
- Volume
- 205
- Issue
- 4
- Pages
- 1939–1973
- Publication date
- 10 February 2026
- Language
- EN