The Mobius Strip Embedding Problem

    Project Details

    Description

    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.
    StatusFinished
    Effective start/end date01/01/199601/10/1996