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 homogeneous foliations on Riemannian symmetric spaces of noncompact type. Apart from the classification result which we proved in [1], we present here in more detail some relevant material about symmetric spaces of noncompact type, and discuss the classification in more detail for the special case M = SL r+1 (R)/SO r+1 .2000 Mathematics Subject Classification. Primary 53C12, 53C35; Secondary 53S20, 22E25.
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