Minimally immersed surfaces in the unit tangent bundle of the 2-sphere arising from area-minimizing unit vector fields on S² \\{N,S} - Conrado, Jackeline (2022)
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.