José Carlos Díaz-Ramos

Real Hypersurfaces with Constant Principal Curvatures in Complex Hyperbolic Spaces

We present the classification of all real hypersurfaces in complex hyperbolic space

Real hypersurfaces with constant principal curvatures in the complex hyperbolic plane

\mathbb{C}H^{n}

Isoparametric hypersurfaces in complex hyperbolic spaces

,

THE STRUCTURE OF ALGEBRAIC COVARIANT DERIVATIVE CURVATURE TENSORS

n \geq 3

Strongly 2-Hopf hypersurfaces in complex projective and hyperbolic planes

, with three distinct constant principal curvatures

Polar Actions on Symmetric Spaces

We classify real hypersurfaces with constant principal curvatures in the complex hyperbolic plane. It follows from this classification that all of them are open parts of homogeneous ones.

On homogeneous manifolds whose isotropy actions are polar

We review some results of an ongoing research on isoparametric hypersurfaces and hypersurfaces with constant principal curvatures in the complex hyperbolic space. In order to motivate this topic, we recall first the main steps of its long history.

Isoparametric submanifolds in two-dimensional complex space forms

We use the Nash embedding theorem to construct generators for the space of algebraic covariant derivative curvature tensors.

Hyperpolar homogeneous foliations on symmetric spaces of noncompact type

We give a geometric characterization of certain hypersurfaces of cohomogeneity one in the complex projective and hyperbolic planes. We also obtain some partial classifications of austere hypersurfaces and of Levi-flat hypersurfaces with constant mean curvature in these spaces.

Almost Kähler Walker 4-manifolds

An isometric action of a connected Lie group H on a Riemannian manifold M is polar if there is exists a connected closed submanifold Σ of M which intersects each orbit of the action and is orthogonal to the orbit at each point of intersection. We present a survey about polar actions on Riemannian symmetric spaces, with emphasis on the noncompact