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Joachimsthal surfaces with nonzero constant Gaussian curvature

Grant number: 21/10181-9
Support type:Scholarships abroad - Research Internship - Post-doctor
Effective date (Start): March 31, 2022
Effective date (End): June 29, 2022
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Ruy Tojeiro de Figueiredo Junior
Grantee:Marcos Paulo Tassi
Supervisor abroad: Jose Antonio Galvez Lopez
Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Research place: Universidad de Granada (UGR), Spain  
Associated to the scholarship:20/03431-6 - Uniqueness of immersed spheres in three-dimensional Riemannian manifolds and Enneper-type hypersurfaces, BP.PD

Abstract

The aim of this project is to investigate Joachimsthal hypersurfaces in R3 with relevant geometric properties, such as constant Gaussian or constant mean curvatures, Weingarten surfaces, etc., in the light of the explicit description of such hypersurfaces in terms of certain differentiable functions of one variable and certain curves in the hyperbolic plane whose coordinate functions satisfy certain second order ODEs, recently obtained by the fellowship holder and his supervisor based on the results obtained by S. Chión and R. Tojeiro in 2021 (see https://arxiv.org/abs/2105.13842). We intend to develop a qualitative study of such ODEs and to investigate global aspects of Joachimsthal surfaces, such as the description of compact examples, in particular those of genus zeroand one.

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