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

2009/10/14 by Mohamed Boucetta, Boucetta, Mohamed · 1 citation
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Advanced Differential Geometry Research

paper · pdf · doi:10.48550/arxiv.0910.2563

Abstract

We determine all Ricci flat left invariant Lorentzian metrics on simply\nconnected 2-step nilpotent Lie groups. We show that the 2k+1-dimensional\nHeisenberg Lie group H_2k+1 carries a Ricci flat left invariant Lorentzian\nmetric if and only if k=1. We show also that for any 2\≤ q\≤ k,\nH_2k+1 carries a Ricci flat left invariant pseudo-Riemannian metric of\nsignature (q,2k+1-q) and we give explicite examples of such metrics.\n

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• Naturally reductive pseudo Riemannian 2-step nilpotent Lie groups

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