学术报告

Double extensions on Riemannian Ricci nilsolitons

发布人:发布时间: 2021-06-10

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题目:Double extensions on Riemannian Ricci nilsolitons


报告人:严再立 教授(宁波大学)

 

时间:202161916:00-17:30

 

地点:西大楼108

 

摘要:A metric Lie algebra (\mathfrak g,< , >) is a Lie algebra \mathfrak g equipped with an indefinite inner product < , >. It  naturally  corresponds to a connected and simply connected Lie group manifold (G,g) with Lie algebra \mathfrak g and left invariant pseudo-Riemannian metric g generated by < , >.

(G,g) (or \mathfrak g,< , >) is said to be an algebraic Ricci soliton if its Ricci operator Ric=c Id+D for some constant real number c and D in Der(\mathfrak g).In the Riemannian case, algebraic Ricci solitons are well understood due to the results of Lauret.  In this talk, we consider Lorentz algebraic Ricci solitons on nilpotent Lie groups.

Based on the concept of Lorentz datum and the technique of double extensions, we are able to construct Lorentz Ricci nilsolitons from any Riemannian Ricci nilsoliton.

Conversely, we show that any Lorentz Ricci nilsoliton with degenerate center is a double extension of a Riemannian Ricci nilsoliton with respect to a Lorentz data. Moreover, we provide a strategy to classify Lorentz   Ricci nilsolitons with degenerate center. This is a joint work with S. Deng.

 

邀请人:胡昊宇 老师