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Miguel Domínguez-Vázquez

Bio: Miguel Domínguez-Vázquez is an academic researcher from University of Santiago de Compostela. The author has contributed to research in topics: Principal curvature & Complex space. The author has an hindex of 9, co-authored 46 publications receiving 227 citations. Previous affiliations of Miguel Domínguez-Vázquez include Spanish National Research Council & Instituto Nacional de Matemática Pura e Aplicada.

Papers
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Journal ArticleDOI
TL;DR: In this paper, a method to study singular Riemannian foliations with closed leaves on complex projective spaces is presented, based on certain graph that generalizes extended Vogan diagrams of inner symmetric spaces.
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.

21 citations

Journal ArticleDOI
TL;DR: In this article, real hypersurfaces in complex space forms with constant principal curvatures and whose Hopf vector field has two nontrivial projections onto the principal curvature spaces are classified.
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. © Indiana University Mathematics Journal.

21 citations

Journal ArticleDOI
TL;DR: In this article, the authors classify polar actions on complex hyperbolic spaces up to orbit equivalence and show that the polar actions can be classified into two classes: (1) this article and (2)
Abstract: We classify polar actions on complex hyperbolic spaces up to orbit equivalence.

20 citations

Journal ArticleDOI
TL;DR: The concept of generalized Kahler angle was introduced in this paper to characterize isoparametric families of hypersurfaces in Damek-Ricci spaces, and it was shown that these examples are inhomogeneous and have nonconstant principal curvatures.

19 citations

Journal ArticleDOI
TL;DR: In this paper, the classification result of real hypersurfaces with constant principal curvatures in nonflat complex space forms and whose Hopf vector field has nontrivial projection onto two eigenspaces of the shape operator was presented.
Abstract: We present the motivation and current state of the classification problem of real hypersurfaces with constant principal curvatures in complex space forms. In particular, we explain the classification result of real hypersurfaces with constant principal curvatures in nonflat complex space forms and whose Hopf vector field has nontrivial projection onto two eigenspaces of the shape operator. This constitutes the following natural step after Kimura and Berndtʼs classifications of Hopf real hypersurfaces with constant principal curvatures in complex space forms.

19 citations


Cited by
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Book ChapterDOI
01 Jan 2015
TL;DR: The study of real hypersurfaces in complex projective space CP n and complex hyperbolic space CH n began at approximately the same time as Munzner's work on isoparametric hypersurface in spheres as discussed by the authors.
Abstract: The study of real hypersurfaces in complex projective space CP n and complex hyperbolic space CH n began at approximately the same time as Munzner’s work on isoparametric hypersurfaces in spheres. A key early work was Takagi’s classification [669] in 1973 of homogeneous real hypersurfaces in CP n . These hypersurfaces necessarily have constant principal curvatures, and they serve as model spaces for many subsequent classification theorems. Later Montiel [501] provided a similar list of standard examples in complex hyperbolic space CH n . In this chapter, we describe these examples of Takagi and Montiel in detail, and later we prove many important classification results involving them. We also study Hopf hypersurfaces, focal sets, parallel hypersurfaces and tubes using both standard techniques of submanifold geometry and the method of Jacobi fields.

228 citations

Book ChapterDOI
01 Oct 2007

131 citations

Book ChapterDOI
01 Jan 2013
TL;DR: In complex hyperbolic geometry, the authors considers an open set biholomorphic to an open ball in Cn, and equip it with a particular metric that makes it have constant negative holomorphic curvature.
Abstract: In complex hyperbolic geometry we consider an open set biholomorphic to an open ball in Cn, and we equip it with a particular metric that makes it have constant negative holomorphic curvature. This is analogous to but different from the real hyperbolic space. In the complex case, the sectional curvature is constant on complex lines, but it changes when we consider real 2-planes which are not complex lines.

96 citations

Proceedings Article
29 May 2014
TL;DR: This work relates elicitability to identifiability (a notion introduced by Osband) and provides a general formula describing all scoring functions for an elicitable property, and draws some connections to the theory of coherent risk measures.
Abstract: Properties of distributions are real-valued functionals such as the mean, quantile or conditional value at risk. A property is elicitable if there exists a scoring function such that minimization of the associated risks recovers the property. We extend existing results to characterize the elicitability of properties in a general setting. We further relate elicitability to identifiability (a notion introduced by Osband) and provide a general formula describing all scoring functions for an elicitable property. Finally, we draw some connections to the theory of coherent risk measures.

73 citations