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arXiv · 2509.10622

The distribution of symmetry of Lorentzian naturally reductive nilmanifolds

Brian Luporini·Silvio Reggiani·Francisco Vittone
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Abstract

We study $2$-step nilpotent Lorentzian Lie groups $N$, which are naturally reductive with respect to a certain class of transitive subgroups of isometries. We describe the isotropy representation and prove that its fixed points give raise to the distribution of symmetry of $N$. This generalizes some known results for the Riemannian case.

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Brian Luporini, Silvio Reggiani, Francisco Vittone. 2025-09-12. The distribution of symmetry of Lorentzian naturally reductive nilmanifolds. https://arxiv.org/abs/2509.10622

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