Homogeneity and canonical connections of isoparametric manifolds (Q1357877)

A geometric construction is given of a connection of an arbitrary isoparametric submanifold \(M\) in a Euclidean space with respect to which the second fundamental form is parallel. It is then proved that \(M\) is an orbit of an \(s\)-representation if and only if the connection is canonical. This continues the study of canonical connections and \(s\)-representations in the papers [J. Reine Angew. Math. 420, 195-202 (1991; Zbl 0727.53012)]\ by \textit{C. Olmos} and \textit{C. Sánchez} and [J. Differ. Geom. 38, 225-234 (1993; Zbl 0791.53051)]\ by \textit{C. Olmos}.