A note on the Gauss map of complete nonorientable minimal surfaces

TL;DR

This paper constructs complete nonorientable minimal surfaces with Gauss maps omitting two points, demonstrating the sharpness of Fujimoto's theorem in the nonorientable case.

Contribution

It provides explicit examples of nonorientable minimal surfaces with Gauss maps omitting two points, confirming the optimality of Fujimoto's theorem for nonorientable surfaces.

Findings

Constructed complete nonorientable minimal surfaces with Gauss maps omitting two points

Confirmed Fujimoto's theorem is sharp for nonorientable minimal surfaces

Advances understanding of the Gauss map behavior in nonorientable minimal surfaces

Abstract

We construct complete nonorientable minimal surfaces whose Gauss map omits two points of the projective plane. This result proves that Fujimoto's theorem is sharp in nonorientable case.