Isoparametric submanifolds and their homogeneous structures
The main problem treated in this interesting paper is the study of the homogeneity of isoparametric submanifolds in a Euclidean space. More precisely, the author considers the link between this problem and the study of the normal holonomy groups of focal manifolds. Using former work of the author and his collaborators on normal holonomy groups and normal homogeneous structures he gives a geometrical proof of the following result of Thorbergsson: Every compact irreducible isoparametric submanifold of a Euclidean space of rank at least 3 is an orbit of an \(s\)-representation (that is, equivalent to the isotropy representation of a semisimple symmetric space). The author also indicates that the same methods can be used to show the homogeneity of irreducible isoparametric submanifolds of higher rank in spaces of constant negative curvature.
scientific article; zbMATH DE number 488223