  The reflection map introduced by D'Angelo is applied to deduce simpler
descriptions of nondegeneracy conditions for sphere maps and to the study of
infinitesimal deformations of sphere maps. It is shown that the dimension of
the space of infinitesimal deformations of a nondegenerate sphere map is
bounded from above by the explicitly computed dimension of the space of
infinitesimal deformations of the homogeneous sphere map. Moreover a
characterization of the homogeneous sphere map in terms of infinitesimal
deformations is provided.
