Non-singular weakly symmetric nilmanifolds

Y. Nikolayevsky; W. Ziller

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arXiv · 2503.01170

Non-singular weakly symmetric nilmanifolds

Y. Nikolayevsky·W. Ziller

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Abstract

A Riemannian manifold $M$ is called weakly symmetric if any two points in $M$ can be interchanged by an isometry. The compact ones have been well understood, and the main remaining case is that of 2-step nilpotent Lie groups. We give a complete classification of simply connected non-singular weakly symmetric nilmanifolds. Besides previously known examples, there are new families with 3-dimensional center, and a one-parameter family of dimensions 14. The classification is based on the authors classification of non-singular 2-step nilpotent Lie groups for which every geodesic is the image of a one parameter group of isometries.

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BibTeX RIS

Y. Nikolayevsky, W. Ziller. 2025-03-03. Non-singular weakly symmetric nilmanifolds. https://arxiv.org/abs/2503.01170

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