The Mobius Strip Embedding Problem

We present necessary and
sufficient conditions for a
curve to be the center curve
of an analytic and flat
embedding of the Mobius strip
(or an orientable cylinder)
into euclidean 3-space.
Using these conditions we
extend an example by G.
Schwarz into a continuous
family of analytic and flat
Mobius strips. This family is
split into two connected
components. We give a
topological argument that
explains this behaviour. A
connection to the work of
C. Chicone and N.J. Kalton on
the Mobius strip embedding
problem, suggests a close
relation between a linking
number and the total torsion
of the orthogonal axes of a
Mobius strip or an orientable
cylinder.