Stiff connections on pseudo-Euclidean spaces
组织者
河井公大朗
, 钱超
演讲者
时间
2023年05月17日 15:20 至 16:20
地点
A3-1-103
线上
Zoom 928 682 9093
(BIMSA)
摘要
Unless it is a flat connection, an affine connection cannot be at the same time projectively flat (geodesics being straight lines) and conformal (conformal structure being preserved by parallel transport). This impossibility is examplified by the two standard models of hyperbolic geometry: Beltrami and Poincaré models.
We define stiff connections by weakening the conformality hypothesis to the requirement that the first order infinitesimal holonomies are infinitesimal isometries. In a given pseudo-Euclidean space, stiff connections are characterized by the choice of a potential and form a continuous family of non-flat connections with surprising properties.
In particular, we prove the existence of a unique affine connection on the disk that is geodesically complete, infinitesimally conformal and projectively flat. This uniquely characterized connection achieves a compromise between properties of Beltrami and Poincaré models of the disk.
演讲者介绍
Tahar是BIMSA助理研究员。在加入BIMSA之前，他曾在魏茨曼科学研究所担任高级博士后研究员。他致力于平面上各种几何结构的模空间研究，包括平移和扩张结构、平坦度规和锥球度规。Guillaume-Tahar最近的研究兴趣涉及线性微分算子、isoresidual fibrations和simplicial arrangements of lines.