Nonlinear Weingarten Surfaces and Flows

• Grant number: 25/09871-1
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: October 01, 2025
• End date: September 30, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Alexandre Paiva Barreto
• Grantee: Rafael da Silva Belli
• Supervisor: Rafael Lopez
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Institution abroad: Universidad de Granada (UGR), Spain
• Associated to the scholarship: 23/06819-3 - Weingarten Hypersurfaces and Flows, BP.DR

Abstract

This research project is divided into two parts:A surface immersed in a Riemannian manifold is called a Weingarten surface when its curvatures satisfy a nontrivial smooth relation. In this part of the project, we are interested in studying nonlinear Weingarten surfaces in 3- and 4-dimensional Riemannian manifolds. More precisely, our main goal is the classification of Darboux surfaces within Thurston's model geometries (and their products) that have constant norm of the second fundamental form.The second part of the project is devoted to the study of the so-called Weingarten flows, which are a natural generalization of the classical mean curvature flow. Our central goal here is the classification of solitons of a Darboux surface with respect to the flow of the norm of the second fundamental form. (AU)