arXiv subjects

Tomas Otero

Publications and source records attributed to Tomas Otero.

3 recordsLinked to original sources

arXiv2026

Cohomogeneity one actions on symmetric spaces of mixed type

In this article, we study isometric cohomogeneity-one actions on symmetric spaces of mixed type, i.e., those whose universal cover splits as a nontrivial product of symmetric spaces of compact, noncompact, and Euclidean types. We provide a new family of "diagonal" cohomogeneity-one actions on symmetric spaces of the form $\mathbb{R}^n \times M_-$, where $M_-$ is of noncompact type. We show that, with the exception of this family, any cohomogeneity-one action on a symmetric space decomposes as a product of isometric actions on its compact, Euclidean, and noncompact factors. This fully reduces the classification problem for cohomogeneity-one actions to symmetric spaces of a single type.

math.DG↗

arXiv2025

Polar actions on homogeneous 3-spaces

We classify polar isometric actions on simply connected 3-dimensional Riemannian homogeneous spaces, up to orbit equivalence. In particular, we classify extrinsically homogeneous surfaces in such spaces and study the geometry of the orbit foliations of the corresponding cohomogeneity one actions.

math.DG↗

arXiv2022

Cohomogeneity one actions on symmetric spaces of noncompact type and higher rank

We develop a new structural result for cohomogeneity one actions on (not necessarily irreducible) symmetric spaces of noncompact type and arbitrary rank. We apply this result to classify cohomogeneity one actions on SL(n,R)/SO(n), n>1, up to orbit equivalence. We also reduce the classification problem on a reducible space to the classification on each one of its irreducible factors, which in particular allows to classify cohomogeneity one actions on any finite product of hyperbolic spaces.

math.DG↗