Sides of the Möbius strip (Q1924939)

The paper presents necessary and sufficient conditions for a curve to be the unique center curve of an analytic and flat embedding of the Möbius strip (or the orientable cylinder) into Euclidean 3-space. Using these conditions, we extend an example of G. Schwarz into a continuous family of analytic and flat Möbius strips. This family is split into two connected components. We give a topological argument that explains this behaviour. Finally, we draw the connection to the work of C. Chicone and N. J. Kalton on flat and analytic Möbius strips. This points towards a connection between a linking number and the total torsion of the orthogonal axis of a Möbius strip.