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Non-singular weakly symmetric nilmanifolds

Y. Nikolayevsky, Wolfgang Ziller

Journal of Lie theory | Jun 17, 2026

Abstract

Abstract

A Riemannian manifold is called weakly symmetric if any two points in M can be interchanged by an isometry. 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.

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Y. Nikolayevsky

first | La Trobe University

Wolfgang Ziller

last | University of Pennsylvania | ORCID 0000-0002-8189-8910

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@article{Nikolayevsky2026singular,
  title = {Non-singular weakly symmetric nilmanifolds},
  author = {Y. Nikolayevsky and Wolfgang Ziller},
  journal = {Journal of Lie theory},
  year = {2026},
  doi = {10.5802/jolt.1424},
  url = {https://doi.org/10.5802/jolt.1424}
}

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