The distribution of symmetry of Lorentzian naturally reductive nilmanifolds

Brian Luporini, Silvio Reggiani, Francisco Vittone

公開日: 2025/9/12

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.