On the Isometry Groups of Invariant Lorentzian Metrics on the Heisenberg Group

作者：del Barco V^*; Ovando G P; Vittone F

来源：Mediterranean Journal of Mathematics, 2014, 11(1): 137-153.

DOI：10.1007/s00009-013-0312-y

• Pseudo-Riemannian spaces
• naturally reductive
• Lie groups
• Heisenberg group

This work concerns the invariant Lorentzian metrics on the Heisenberg Lie group of dimension three and the bi-invariant metrics on the solvable Lie groups of dimension four. We start with the indecomposable Lie groups of dimension four admitting bi-invariant metrics and which act on by isometries and we study some geometrical features on these spaces. On , we prove that the property of the metric being proper naturally reductive is equivalent to the property of the center being non-degenerate. These metrics are Lorentzian algebraic Ricci solitons.

• 出版日期2014-2