  Supertwistor theory is geometrically constructed based on the SUSY Hopf map.
We derive a new incidence relation for the geometrical supertwistor theory. The
present supertwistor exhibits remarkable properties: Minkowski space need not
be complexified to introduce spin degrees of freedom, and even number SUSY is
{automatically} incorporated by the geometrical set-up. We also develop a
theory for massless free particle in Minkowski superspace, which physically
corresponds to the geometrical supertwistor theory. The spin degrees of freedom
are originated from fermionic momenta as well as fermionic coordinates. The
geometrical supertwistor is quantized to reproduce same physical contents as in
the original supertwistor theory. Relationships to superspin formalism and SUSY
quantum Hall effect are also discussed.
