Surfaces of Enneper type

Author(s)

Alan Sousa França

• Document type: Master's Dissertation
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2023-02-16

Examining board members

Ruy Tojeiro de Figueiredo Junior; Alexandre Paiva Barreto; Igor Mencattini; Walcy Santos

• Advisor: Ruy Tojeiro de Figueiredo Junior; Marcos Paulo Tassi

Abstract

We study surfaces free of umbilical points in the 3-dimensional Euclidean space with the lines of curvature of one family contained in planes or spheres, called surfaces of Enneper type. We present a parametrization of the surfaces with planar lines of curvature and describe how an arbitrary surface of Enneper type can be constructed from a surface of Enneper type with one family of planar lines of curvature. We obtain a new description of the special class of surfaces of Enneper type with the property that the spheres that contain the lines of curvature correspondent to one of its principal curvatures are all centered on a common straight line. In particular, this class includes the nonzero constant Gaussian curvature ones. We also discuss the classification of the minimal surfaces of Enneper type. (AU)

• FAPESP's process: 21/03304-7 - Enneper surfaces
• Grantee: Alan Sousa França
• Support Opportunities: Scholarships in Brazil - Master