Homogeneous Lorentzian structures of 4-dimensional nilpotent Lie groups
Volume 131 / 2023
Annales Polonici Mathematici 131 (2023), 263-294
MSC: Primary 53C50; Secondary 53B30
DOI: 10.4064/ap221207-21-8
Published online: 27 November 2023
Abstract
We consider the four-dimensional 2-step nilpotent Lie group $H_{3}\times \mathbb {R}$, equipped with a family of non-flat left-invariant Lorentzian metrics. We give a complete classification of all homogeneous structures for each metric. We then investigate the properties of each structure and prove the existence of a non-canonical homogeneous structure. Finally, we present an example of a naturally reductive, non-flat, left-invariant Lorentzian metric on $H_{3}\times \mathbb {R}$ for which the center is degenerate.
