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

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• 作者：V. del Barco (1)
  G. P. Ovando (1)
  F. Vittone (1)
  
• 关键词：53C50 ; 53C30 ; 22E25 ; 57S25 ; Pseudo ; Riemannian spaces ; naturally reductive ; Lie groups ; Heisenberg group
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2014
• 出版时间：February 2014
• 年：2014
• 卷：11
• 期：1
• 页码：137-153
• 全文大小：296 KB
• 作者单位：V. del Barco (1)
  G. P. Ovando (1)
  F. Vittone (1)
  
  1. Depto de Matem谩tica, ECEN-FCEIA, Universidad Nacional de Rosario, Pellegrini 250, 2000, Rosario, Santa Fe, Argentina
  
• ISSN：1660-5454

文摘

This work concerns the invariant Lorentzian metrics on the Heisenberg Lie group of dimension three ${{\rm H}_3(\mathbb{R})}$ 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 ${{\rm H}_3(\mathbb{R})}$ by isometries and we study some geometrical features on these spaces. On ${{\rm H}_3(\mathbb{R})}$ , 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.