On quadratic isoparametric submanifolds (Q1210498)

The author investigates homogeneity of quadratic isoparametric submanifolds and gives a partial classification of quadratic isoparametric systems. He proves that each closed quadratic isoparametric submanifold \(M^ n\subset\mathbb{R}_ p^{n+m}\) is extrinsically symmetric, especially it is homogeneous. In another paper [Glasg. Math. J. 35, 135- 143 (1993; Zbl 0783.53027)], the author showed that each full quadratic isoparametric submanifold determines a quadratic isoparametric system. Using this relationship, in his theorem 3.1 he classifies full and irreducible quadratic isoparametric submanifolds.