Homogeneous and inhomogeneous isoparametric hypersurfaces in rank one symmetric spaces

Se p 20 01 Homogeneous Spaces , Tits Buildings , and Isoparametric Hypersurfaces

We classify 1-connected compact homogeneous spaces which have the same rational cohomology as a product of spheres S1 × S2 , with 3 ≤ n1 ≤ n2 and n2 odd. As an application, we classify compact generalized quadrangles (buildings of type C2) which admit a point transitive automorphism group, and isoparametric hypersurfaces which admit a transitive isometry group on one focal manifold. Received by...

Cohomogeneity One Actions on Noncompact Symmetric Spaces of Rank One

We classify, up to orbit equivalence, all cohomogeneity one actions on the hyperbolic planes over the complex, quaternionic and Cayley numbers, and on the complex hyperbolic spaces CHn, n ≥ 3. For the quaternionic hyperbolic spaces HHn, n ≥ 3, we reduce the classification problem to a problem in quaternionic linear algebra and obtain partial results. For real hyperbolic spaces, this classificat...

Homogeneous Hypersurfaces in Complex Hyperbolic Spaces

We study the geometry of homogeneous hypersurfaces and their focal sets in complex hyperbolic spaces. In particular, we provide a characterization of the focal set in terms of its second fundamental form and determine the principal curvatures of the homogeneous hypersurfaces together with their multiplicities.

Curvature Characterization and Classification of Rank-one Symmetric Spaces

Ford Fundamental Domains in Symmetric Spaces of Rank One

We show the existence of isometric (or Ford) fundamental regions for a large class of subgroups of the isometry group of any rank one Riemannian symmetric space of noncompact type. The proof does not use the classification of symmetric spaces. All hitherto known existence results of isometric fundamental regions and domains are essentially subsumed by our work.