Minimally immersed surfaces in the unit tangent bundle of the 2-sphere arising from area-minimizing unit vector fields on S² \\{N,S}

• Autor(a) principal: Conrado, Jackeline
• Data de Publicação: 2022
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: https://www.teses.usp.br/teses/disponiveis/45/45131/tde-18112022-233840/
• topic: Clifford torus; Espaço projetivo redondo; Fibrado tangente unitário; Garrafa de Klein; Klein bottle; Minimal surface; Round projective space; Superfícies mínimas; Toro de Clifford; Unit tangent bundle; Volume de campos vetoriais unitários; Volume of a unit vector field

The aim of this work is twofold. Firstly, for the unit vector fields on S²\\{N,S} with even Poincaré indexes other than zero or two, we prove that the topological closure of their image coincides with the image of minimally immersed Klein bottles in T¹S². Secondly, we establish a relationship between the Clifford Torus and the North-South and South-North unit vector field. More specifically, we prove that the topological closure of the union of the images of the North-South and the South-North vector fields in T¹S² is an embedded Clifford Torus.