四元数射影空间上的一类等参超曲面

A Class of Isoparametric Hypersurfaces in Quaternion Projective Space

利用ＱＰ～ｎ上实超曲面与其在Ｓ（４ｎ＋３）上的Ｈｏｐｆ原像的形状算子间的关系，讨论了四元数射影空问ＱＰ～ｎ上的等参超曲面，指出ＱＰ～ｎ上的某些等参超曲面之不同主曲率个数函数ｇ不为常数．

The isoparametric hypersurfaces in quaternion projective spaces QPn are discussed by using the relationship between the two shape operators of a real hypersurface in QPn and its inverse image under the Hopf map in S^4n+3. And the nonconstancy of the number functions of distinct principal curvatures of some isoparametric hypersurfaces in QPn is Pointed.