  We study the Gauss map and the dual variety of a real-analytic immersion of a
connected compact real-analytic manifold into a sphere or into a hyperbolic
space. The dual variety is defined to be the set of all normal directions of
the immersion. First, we show that the image of the Gauss map characterizes the
manifold. Also we show that the dual variety characterizes the manifold.
Besides, duality of the second fundamental form and some results on
degeneration are obtained. In Algebraic Geometry E-prints eight files are
tar-compressed and uuencoded.
