A class of totally geodesic foliations of Lie groups (Q914165)

Let G be a compact, connected, simply-connected Lie group, and let K be a connected closed subgroup of G such that G/K is a rank-1 Riemannian symmetric space. This paper is devoted to classifying the foliations of G with leaves of the form \(gKh^{-1}\). In the case when \(G/K=S^ n\), the homotopy type of the space of such foliations is also given. This work generalizes that of \textit{H. Gluck} and \textit{F. W. Warner} [Duke Math. J. 50, 107-132 (1983; Zbl 0523.55020)] concerning the great circle fibrations of the three sphere.