Polar homogeneous foliations on symmetric spaces of rank one
We classify polar homogeneous foliations on rank one symmetric spaces of noncompact type up to orbit equivalence.
math.DG↗
arXiv subjects
José Carlos Díaz-Ramos
Publications and source records attributed to José Carlos Díaz-Ramos.
Codimension two polar homogeneous foliations on symmetric spaces of noncompact type
We classify homogeneous polar foliations of codimension two on irreducible symmetric spaces of noncompact type up to orbit equivalence. Any such foliation is either hyperpolar or the canonical extension of a polar homogeneous foliation on a rank one symmetric space.
math.DG↗
The Ambrose-Singer Theorem for cohomogeneity one Riemannian manifolds
We characterize isometric actions whose principal orbits are hypersurfaces through the existence of a linear connection satisfying a set of covariant equations in the same spirit as the Ambrose-Singer Theorem for homogeneous space. These results are then used to describe isometric cohomogeneity one foliations in terms of such connections. Finally, we provide explicit examples of these objects in Euclidean spaces and real hyperbolic spaces.
math.DG↗