Generalized Ricci surfaces
Organizers
Speaker
Yiming Zang
Time
Monday, May 27, 2024 3:00 PM - 5:00 PM
Venue
A3-4-301
Online
Zoom 435 529 7909
(BIMSA)
Abstract
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.