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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Keywords: non-singular nilmanifold, weakly symmetric manifold
Nikolayevsky, Yuri 1 ; Ziller, Wolfgang 2
Nikolayevsky, Yuri; Ziller, Wolfgang. Non-singular weakly symmetric nilmanifolds. Journal of Lie Theory, Special issue dedicated to the memory of Joseph A. Wolf, Volume 36 (2026) no. 1, pp. 201-211. doi: 10.5802/jolt.1424
@article{10_5802_jolt_1424,
author = {Nikolayevsky, Yuri and Ziller, Wolfgang},
title = {Non-singular weakly symmetric nilmanifolds},
journal = {Journal of Lie Theory},
pages = {201--211},
year = {2026},
publisher = {XXXX},
volume = {36},
number = {1},
doi = {10.5802/jolt.1424},
language = {en},
url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1424/}
}
TY - JOUR AU - Nikolayevsky, Yuri AU - Ziller, Wolfgang TI - Non-singular weakly symmetric nilmanifolds JO - Journal of Lie Theory PY - 2026 SP - 201 EP - 211 VL - 36 IS - 1 PB - XXXX UR - https://jolt.centre-mersenne.org/articles/10.5802/jolt.1424/ DO - 10.5802/jolt.1424 LA - en ID - 10_5802_jolt_1424 ER -
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