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Generalized Ricci surfaces

组织者

杨琳 , 塞巴斯蒂安·赫勒 , 河井公大朗

演讲者

臧艺茗

时间

2024年05月27日 15:00 至 17:00

地点

A3-4-301

线上

Zoom 435 529 7909 (BIMSA)

摘要

We consider smooth Riemannian surfaces whose curvature $K$ satisfies the equation $\Delta\log|K-c|=aK+b$ away from points where $K=c$ for some $(a,b,c)\in\mathbb{R}^3$, which we call generalized Ricci surfaces. This equation generalize a result of Ricci, which provides a necessary and sufficient condition for the surface to be (locally) minimally and isometrically immersed in Euclidean $3$-space. In the first part of this talk, we prove some basic properties of generalized Ricci surfaces, in order to show that these surfaces are related to many geometric objects. In the second part, we mainly focus on compact generalized Ricci surfaces: we obtain topological obstructions and construct examples. This is a joint work with Benoit Daniel.