25 citations · 36 across the 17 of their papers we have counts for
24 papers
Polar actions on homogeneous 3-spaces
Miguel Dominguez-Vazquez, Tarcios A. Ferreira, Tomas Otero
We classify polar isometric actions on simply connected 3-dimensional Riemannian homogeneous spaces, up to orbit equivalence. In particular, we classify extrinsically homogeneous s…
On isoparametric foliations of complex and quaternionic projective spaces
Miguel Dominguez-Vazquez, Andreas Kollross
We conclude the classification of isoparametric (or equivalently, polar) foliations of complex and quaternionic projective spaces. This is done by investigating the projections of…
Cohomogeneity one actions on symmetric spaces of noncompact type and higher rank
Jose Carlos Diaz-Ramos, Miguel Dominguez-Vazquez, Tomas Otero
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 cl…
Isoparametric hypersurfaces in symmetric spaces of non-compact type and higher rank
Miguel Dominguez-Vazquez, Victor Sanmartin-Lopez
We construct inhomogeneous isoparametric families of hypersurfaces with non-austere focal set on each symmetric space of non-compact type and rank greater than or equal to 3. If th…
Codimension one Ricci soliton subgroups of solvable Iwasawa groups
Miguel Dominguez-Vazquez, Victor Sanmartin-Lopez, Hiroshi Tamaru
Recently, Jablonski proved that, to a large extent, a simply connected solvable Lie group endowed with a left-invariant Ricci soliton metric can be isometrically embedded into the…
Existence and uniqueness of inhomogeneous ruled hypersurfaces with shape operator of constant norm in the complex hyperbolic space
Miguel Dominguez-Vazquez, Olga Perez-Barral
We complete the classification of ruled real hypersurfaces with shape operator of constant norm in nonflat complex space forms by showing the existence of a unique inhomogeneous ex…
Homogeneous CR submanifolds of complex hyperbolic spaces
Jose Carlos Diaz-Ramos, Miguel Dominguez-Vazquez, Olga Perez-Barral
We classify homogeneous CR submanifolds in complex hyperbolic spaces arising as orbits of a subgroup of the solvable part of the Iwasawa decomposition of the isometry group of the…
Homogeneous Lagrangian foliations on complex space forms
Jose Carlos Diaz-Ramos, Miguel Dominguez-Vazquez, Takahiro Hashinaga
We classify holomorphic isometric actions on complex space forms all whose orbits are Lagrangian submanifolds, up to orbit equivalence. The only examples are Lagrangian affine subs…
Homogeneous and inhomogeneous isoparametric hypersurfaces in rank one symmetric spaces
Jose Carlos Diaz-Ramos, Miguel Dominguez-Vazquez, Alberto Rodriguez-Vazquez
We conclude the classification of cohomogeneity one actions on symmetric spaces of rank one by classifying cohomogeneity one actions on quaternionic hyperbolic spaces up to orbit e…
Submanifold geometry in symmetric spaces of noncompact type
Jose Carlos Diaz-Ramos, Miguel Dominguez-Vazquez, Victor Sanmartin-Lopez
In this survey article we provide an introduction to submanifold geometry in symmetric spaces of noncompact type. We focus on the construction of examples and the classification pr…
On homogeneous manifolds whose isotropy actions are polar
Jose Carlos Diaz-Ramos, Miguel Dominguez-Vazquez, Andreas Kollross
We show that simply connected Riemannian homogeneous spaces of compact semisimple Lie groups with polar isotropy actions are symmetric, generalizing results of Fabio Podesta and th…
Ruled hypersurfaces with constant mean curvature in complex space forms
Miguel Dominguez-Vazquez, Olga Perez-Barral
We show that ruled real hypersurfaces with constant mean curvature in the complex projective and hyperbolic spaces must be minimal. This provides their classification, by virtue of…
Solutions to the overdetermined boundary problem for semilinear equations with position-dependent nonlinearities
Miguel Dominguez-Vazquez, Alberto Enciso, Daniel Peralta-Salas
We show that a wide range of overdetermined boundary problems for semilinear equations with position-dependent nonlinearities admits nontrivial solutions. The result holds true bot…
Strongly 2-Hopf hypersurfaces in complex projective and hyperbolic planes
Jose Carlos Diaz-Ramos, Miguel Dominguez-Vazquez, Cristina Vidal-Castiñeira
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 a…
Isoparametric submanifolds in two-dimensional complex space forms
Jose Carlos Diaz-Ramos, Miguel Dominguez-Vazquez, Cristina Vidal-Castiñeira
We show that an isoparametric submanifold of a complex hyperbolic plane, according to the definition of Heintze, Liu and Olmos', is an open part of a principal orbit of a polar act…
Isoparametric hypersurfaces in complex hyperbolic spaces
Jose Carlos Diaz-Ramos, Miguel Dominguez-Vazquez, Victor Sanmartin-Lopez
We classify isoparametric hypersurfaces in complex hyperbolic spaces.
Polar foliations on quaternionic projective spaces
Miguel Dominguez-Vazquez, Claudio Gorodski
We classify irreducible polar foliations of codimension on quaternionic projective spaces , for all . We prove that all irreducible polar foliati…
Canonical extension of submanifolds and foliations in noncompact symmetric spaces
Miguel Dominguez-Vazquez
We propose a method to extend submanifolds, singular Riemannian foliations and isometric actions from a boundary component of a noncompact symmetric space to the whole space. This…
Cohomogeneity one actions on some noncompact symmetric spaces of rank two
Jurgen Berndt, Miguel Dominguez-Vazquez
We classify, up to orbit equivalence, the cohomogeneity one actions on the noncompact duals of the symmetric spaces G_2, SU_3 and the real oriented two-plane Grassmannians.
Real hypersurfaces with two principal curvatures in complex projective and hyperbolic planes
J. Carlos Diaz-Ramos, Miguel Dominguez-Vazquez, Cristina Vidal-Castiñeira
We find the first examples of real hypersurfaces with two nonconstant principal curvatures in complex projective and hyperbolic planes, and we classify them. It turns out that each…
Isoparametric foliations on complex projective spaces
Miguel Dominguez-Vazquez
Irreducible isoparametric foliations of arbitrary codimension q on complex projective spaces CP^n are classified, except if n=15 and q=1. Remarkably, there are noncongruent example…
Isoparametric hypersurfaces in Damek-Ricci spaces
J. Carlos Diaz-Ramos, Miguel Dominguez-Vazquez
We construct uncountably many isoparametric families of hypersurfaces in Damek-Ricci spaces. We characterize those of them that have constant principal curvatures by means of the n…
Inhomogeneous isoparametric hypersurfaces in complex hyperbolic spaces
J. Carlos Diaz-Ramos, Miguel Dominguez-Vazquez
We construct examples of inhomogeneous isoparametric real hypersurfaces in complex hyperbolic spaces.
Non-Hopf real hypersurfaces with constant principal curvatures in complex space forms
Jose Carlos Diaz-Ramos, Miguel Dominguez-Vazquez
We classify real hypersurfaces in complex space forms with constant principal curvatures and whose Hopf vector field has two nontrivial projections onto the principal curvature spa…