[geometry-ml:05794] OCAMI 微分幾何学セミナー 2024/07/19

[TAMARU, Hiroshi]

幾何学 ML のみなさま：

大阪公立大学の田丸です。

下記の要領で OCAMI 微分幾何学セミナー
https://www.omu.ac.jp/orp/ocami/activities/seminars/dg/
を開催します。会場は大阪公立大学杉本キャンパスです。

みなさまの参加をお待ちしております。
どうぞよろしくお願いいたします。

*****
日時	2024年7月19日（金）16:45-18:15
講演者（所属）	Wafaa Batat (Ecole Nationale Polytechnique d'Oran Maurice 
Audin)
タイトル	Homogeneous Structures on Three- and Four-dimensional Lie groups
場所	理学部F棟4階 小講究室B（F405）
アブストラクト	In this talk, we will introduce the notion of homogeneous 
pseudo-Riemannian structures and demonstrate how to establish 
homogeneity and natural reductiveness of 3- and 4-dimensional Lie groups 
through a tensor satisfying certain geometric partial differential 
equations involving the metric and the curvature of a given manifold. 
These equations are known as Ambrose-Singer equations. We will begin by 
examining homogeneous structures on three-dimensional unimodular and 
non-unimodular Lie groups, proving the existence of homogeneous 
Lorentzian structures that differ from the canonical ones without being 
naturally reductive, a phenomenon with no Riemannian counterpart. Using 
these homogeneous structures, we will show how to classify naturally 
reductive 3-dimensional Lorentzian manifolds. Our focus will then shift 
to the geometric properties of four-dimensional nilpotent Lie groups 
endowed with a family of non-flat left-invariant Lorentzian metrics. We 
will conduct a comprehensive classification of homogeneous structures 
for each metric and meticulously examine the distinctive properties 
characterizing each structure. Additionally, we will provide a specific 
example demonstrating the presence of a naturally reductive, non-flat, 
left-invariant Lorentzian metric on the 2-nilpotent Lie group, where the 
center exhibits degeneracy. Furthermore, we will establish the existence 
of a non-canonical homogeneous structure. As an application, we will 
demonstrate the existence of naturally reductive left-invariant 
Lorentzian metrics on the four-dimensional 3-nilpotent Lie group.

-- 
田丸博士
大阪公立大学理学研究科
---
Hiroshi TAMARU
Osaka Metropolitan University
https://www.omu.ac.jp/sci/tamaru/