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A foliation F on a Riemannian manifold M is homogeneous if its leaves coincide with the orbits of an isometric action on M . A foliation F is polar if it admits a section, that is, a connected closed totally geodesic submanifold of M which intersects each leaf of F , and intersects orthogonally at each point of intersection. A foliation F is hyperpolar if it admits a flat section. These notes are related to joint work with José Carlos Díaz-Ramos and Hiroshi Tamaru about hyperpolar homogeneousdoi:10.4310/jdg/1299766787 fatcat:ypnafxpotjb55n2p5ez52gezsq