Corpus ID: 115171916

Ricci flat left invariant Lorentzian metrics on 2-step nilpotent Lie groups

@article{Boucetta2009RicciFL,
  title={Ricci flat left invariant Lorentzian metrics on 2-step nilpotent Lie groups},
  author={M. Boucetta},
  journal={arXiv: Differential Geometry},
  year={2009}
}
  • M. Boucetta
  • Published 2009
  • Mathematics, Physics
  • arXiv: Differential Geometry
  • We determine all Ricci flat left invariant Lorentzian metrics on simply connected 2-step nilpotent Lie groups. We show that the $2k+1$-dimensional Heisenberg Lie group $H_{2k+1}$ carries a Ricci flat left invariant Lorentzian metric if and only if $k=1$. We show also that for any $2\leq q\leq k$, $H_{2k+1}$ carries a Ricci flat left invariant pseudo-Riemannian metric of signature $(q,2k+1-q)$ and we give explicite examples of such metrics. 

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