تحت إشراف قسم الرياضيات والإحصاء وبالتعاون مع مركز البحوث بالكلية أقيم اليوم الثلاثاء 18 / 2 / 2020 سيمنار بعنوان :

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

قدمته  د. منى بن عصفور وذلك في تمام الساعة ٩:٠٠ ص في قاعة الاجتماعات بكلية العلوم.

ملخص البحث :

The purpose of this reasach is to investigate Ricci-flatness of left-invariant Lorentzian metrics on 2-step nilpotent Lie groups. We first show that if <,> is a Ricci-flat left-invariant Lorentzian metric on a 2-step nilpotent Lie group N, then the restriction of <,> to the center of the Lie algebra of N is degenerate. We then characterize the 2-step nilpotent Lie groups which can be endowed with a Ricci-flat left-invariant Lorentzian metric, and we deduce from this that a Heisenberg Lie group H2n+1 can be endowed with Ricci-flat left-invariant Lorentzian metric if and only if n = 1. We also show that the free 2-step nilpotent Lie group on m generators Nm,2 admits a Ricci-flat left-invariant Lorentzian metric if and only if m = 2 or m = 3, and we determine all Ricci-flat left-invariant Lorentzian metrics on the free 2-step nilpotent Lie group on 3 generators N3,2.

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