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

摘要: 利用_QPⁿ上实超曲面与其在S⁴ⁿ⁺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_QPⁿ上的等参超曲面,指出_QPⁿ上的某些等参超曲面之不同主曲率个数函数g不为常数.

Abstract: 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 S⁴ⁿ⁺³. And the nonconstancy of the number functions of distinct principal curvatures of some isoparametric hypersurfaces in _QPⁿ is Pointed.