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arXiv · 0910.2563

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

Mohamed Boucetta
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Abstract

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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Mohamed Boucetta. 2010-02-15. Ricci flat left invariant Lorentzian metrics on 2-step nilpotent Lie groups. https://arxiv.org/abs/0910.2563

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