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

The reflection map and infinitesimal deformations of sphere mappings