The distribution of symmetry of Lorentzian naturally reductive nilmanifolds

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.