球面中等参超曲面及其焦流形的有限性定理

A Finiteness Theorem for Isoparametric Hypersurfaces and Focal Submanifolds in Spheres

球面中等参超曲面理论近期获得蓬勃发展,它们在等距意义下的分类至今未完全解决,将证明球面中等参超曲面及其焦流形的微分同胚型有限.

Recently, the theory of isoparametric hypersurfaces in spheres have developed greatly. Their classification up to isometry has not completely been solved yet. In this paper, we will prove that there are only finitely many diffeomorphism classes of isoparametric hypersurfaces and of focal submanifolds in a sphere.