球面映射的反射映射与无穷小变形
The reflection map and infinitesimal deformations of sphere mappings
摘要：
D'Angelo引入的反射映射被用来推导球面映射非退化条件的简单描述和研究球面映射的无穷小形变。证明了非退化球面映射的无穷小变形空间的维数由齐次球面映射的无穷小变形空间的显式计算维数从上而下有界。此外，还给出了齐次球面映射的无穷小形变的一个刻画。
英文摘要：
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.
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