Hyperpolar homogeneous foliations on symmetric spaces of noncompact type

Jürgen Berndt, José Carlos Díaz-Ramos, Hiroshi Tamaru
2010 Journal of differential geometry  
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
more » ... polar 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 = SLr+1(R)/SOr+1. Key words and phrases: Riemannian symmetric spaces of noncompact type, homogeneous foliations, hyperpolar foliations, polar foliations, horospherical decompositions.
doi:10.4310/jdg/1299766787 fatcat:ypnafxpotjb55n2p5ez52gezsq