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报告地址：行健楼学术活动室665

邀请人：陈慧斌 副教授

报告摘要: We Present a classication of simply connected essential conformally homogeneous Lorentzian manifolds, that is Lorentzian manifolds (M, g) which admit an essential transitive group G of conformal transformations. This means that the group G does not preserves any metric f(x)g, 0 < f(x) ∈ C^∞ (M), conformal to g . Following A-2017, Note di Mat.), we consider two types of Lorentzian essential conformally homogeneous manifolds (M = G/H, [g])

A. Manifolds with non-faithful isotropy representation

j : H → CO(V ), V = ToM = g / h of the stability subgroup H .

B. Manifolds with faithful isotropy representation j .

We present some results about type A) Lorentzian, and ,more generally, pseudo-Riemnaian essential conformally homogeneous manifolds (M = G/H, g) of any signature. In partucular, the result that any Lorentzian essential conformally homogeneous manifold is conformally at. Then we present the classication of Lorentzian essential conformally homogeneous manifold of type B). The main result states that any such manifold is a plane wave. More precisely, the following theorem holds.

The main theorem. Let (M = G/H, c = [g]) be a simply connected Lorentzian conformal manifold with a transitive conformal group G of type B).Then there is a metric g 0 ∈ c from the conformal class c such that (M = G/H, g o ) is a homogeneous Lorentzian plane wave manifold. Moreovere, the connected group of conformal transformations consists of homotheties, and it is a 1-dimensional extension of the group of isometries.

We recall the denition and the main properties of homogeneous plane waves and indicate the main steps of the proof of the theorem.

报告人简介：Dmitri Alekseevsky教授是国际著名的俄罗斯数学家，现任俄罗斯科学院斯捷克洛夫数学研究所首席研究员，并在俄罗斯国立高等经济大学（HSE）担任微分几何与拓扑学教席。作为李群理论、齐性几何结构及超对称场论领域的先驱学者，他的研究深刻影响了现代微分几何、理论物理与数学物理的交叉发展。

Alekseevsky教授早年毕业于莫斯科国立大学，师从苏联几何学派代表人物之一。他的代表性工作包括：

* 对齐性伪黎曼空间的分类，揭示了对称空间与爱因斯坦方程的新联系；

* 提出超对称规范场的几何模型，为弦论与超引力理论提供数学基础；

* 建立特殊几何流形的全局理论，推动可积系统与几何分析的融合。

他是《Journal of Geometry and Physics》编委，Springer数学专著系列顾问，并主导多项欧洲与俄罗斯基础科学合作项目。因其卓越贡献，他于2001年当选俄罗斯科学院通讯院士，2018年获俄罗斯联邦国家科学奖（数学领域最高荣誉），并被授予意大利国际理论物理中心（ICTP）终身荣誉研究员称号。