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Search Results: 1 - 10 of 17608 matches for " Miguel Dominguez-Vazquez "
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Canonical extension of submanifolds and foliations in noncompact symmetric spaces
Miguel Dominguez-Vazquez
Mathematics , 2014,
Abstract: 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 extension method preserves minimal submanifolds, isoparametric foliations and polar actions, among other properties. One of the several applications yields the first examples of inhomogeneous isoparametric hypersurfaces in noncompact symmetric spaces of rank at least two.
Isoparametric foliations on complex projective spaces
Miguel Dominguez-Vazquez
Mathematics , 2012,
Abstract: 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 examples that pull back under the Hopf map to congruent foliations on the sphere. Moreover, there exist many inhomogeneous isoparametric foliations, even of higher codimension. In fact, every irreducible isoparametric foliation on the complex projective n-space is homogeneous if and only if n+1 is prime. The main tool developed in this work is a method to study singular Riemannian foliations with closed leaves on complex projective spaces. This method is based on certain graph that generalizes extended Vogan diagrams of inner symmetric spaces.
Cohomogeneity one actions on some noncompact symmetric spaces of rank two
Jurgen Berndt,Miguel Dominguez-Vazquez
Mathematics , 2013,
Abstract: 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.
Polar foliations on quaternionic projective spaces
Miguel Dominguez-Vazquez,Claudio Gorodski
Mathematics , 2015,
Abstract: We classify irreducible polar foliations of codimension $q$ on quaternionic projective spaces $\mathbb H P^n$, for all $(n,q)\neq(7,1)$. We prove that all irreducible polar foliations of any codimension (resp. of codimension one) on $\mathbb H P^n$ are homogeneous if and only if $n+1$ is a prime number (resp. $n$ is even or $n=1$). This shows the existence of inhomogeneous examples of codimension one and higher.
Inhomogeneous isoparametric hypersurfaces in complex hyperbolic spaces
J. Carlos Diaz-Ramos,Miguel Dominguez-Vazquez
Mathematics , 2010,
Abstract: 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
Mathematics , 2009,
Abstract: 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 spaces. In complex projective spaces such real hypersurfaces do not exist. In complex hyperbolic spaces these are holomorphically congruent to open parts of tubes around the ruled minimal submanifolds with totally real normal bundle introduced by Berndt and Bruck. In particular, they are open parts of homogenous ones.
Isoparametric hypersurfaces in Damek-Ricci spaces
J. Carlos Diaz-Ramos,Miguel Dominguez-Vazquez
Mathematics , 2011,
Abstract: 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 new concept of generalized Kahler angle. It follows that, in general, these examples are inhomogeneous and have nonconstant principal curvatures. We also find new cohomogeneity one actions on quaternionic hyperbolic spaces, and an isoparametric family of inhomogeneous hypersurfaces with constant principal curvatures in the Cayley hyperbolic plane.
Polar actions on complex hyperbolic spaces
J. Carlos Diaz-Ramos,Miguel Dominguez-Vazquez,Andreas Kollross
Mathematics , 2012,
Abstract: We classify polar actions on complex hyperbolic spaces up to orbit equivalence.
Isoparametric hypersurfaces in complex hyperbolic spaces
Jose Carlos Diaz-Ramos,Miguel Dominguez-Vazquez,Victor Sanmartin-Lopez
Mathematics , 2015,
Abstract: We classify isoparametric hypersurfaces in complex hyperbolic spaces.
Real hypersurfaces with two principal curvatures in complex projective and hyperbolic planes
J. Carlos Diaz-Ramos,Miguel Dominguez-Vazquez,Cristina Vidal-Casti?eira
Mathematics , 2013,
Abstract: 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 such hypersurface is foliated by equidistant Lagrangian flat surfaces with parallel mean curvature or, equivalently, by principal orbits of a cohomogeneity two polar action.
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