Flat Moebius strips of given isotopy types in R^3 whose centerlines are geodesics or lines of curvature

TL;DR

This paper constructs real analytic flat Moebius strips in three-dimensional space with any given isotopy type, ensuring their centerlines are either geodesics or lines of curvature, advancing geometric understanding of these surfaces.

Contribution

It introduces a method to construct flat Moebius strips with arbitrary isotopy types having centerlines as geodesics or lines of curvature, which was not previously established.

Findings

Successfully constructed flat Moebius strips with arbitrary isotopy types

Centerlines are either geodesics or lines of curvature

Surfaces are real analytic

Abstract

We construct real analytic flat Moebius strips of arbitrary isotopy types, whose centerlines are geodesics or lines of curvature.