October 13, 2025Open Access

The distribution of symmetry of Lorentzian naturally reductive nilmanifolds

BLBrian Luporini SRSilvio ReggianiConsejo Nacional de Investigaciones Científicas y Técnicas FVFrancisco VittoneConsejo Nacional de Investigaciones Científicas y Técnicas

Key Points

Symmetry distribution of nilmanifolds is influenced by isotropy conditions and 2-step nilpotency.
Key results extend findings known from the Riemannian context to the Lorentzian framework.
The isotropy representation provides essential insights into the geometric structure of these Lie groups.
Understanding these dynamics could have broader implications in geometric analysis and mathematical physics.

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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