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Search Results: 1 - 10 of 7479 matches for " Claudio Gorodski "
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Taut submanifolds
Gorodski,Claudio;
Revista de la Uni?3n Matem??tica Argentina , 2006,
Abstract: this is a short, elementary survey article about taut submanifolds. in order to simplify the exposition, we restrict to the case of compact smooth submanifolds of euclidean or spherical spaces. some new, partial results concerning taut 4-manifolds are discussed at the end of the text.
A class of complete embedded minimal submanifolds in noncompact symmetric spaces
Claudio Gorodski
Mathematics , 2001,
Abstract: We show that a totally geodesic submanifold of a symmetric space satisfying certain conditions admits an extension to a minimal submanifold of dimension one higher, and we apply this result to construct new examples of complete embedded minimal submanifolds in simply connected noncompact globally symmetric spaces.
Jacobi fields on normal homogeneous Riemannian manifolds
Claudio Gorodski
Mathematics , 2005,
Abstract: We prove that a normal homogeneous space with the property that every Jacobi field along a geodesic vanishing at two points is the restriction of a Killing field along that geodesic is a globally symmetric space.
Taut submanifolds
Claudio Gorodski
Mathematics , 2006,
Abstract: This is a short, elementary survey article about taut submanifolds. In order to simplify the exposition, we restrict to the case of compact smooth submanifolds of Euclidean or spherical spaces. Some new, partial results concerning taut 4-manifolds are discussed at the end of the text.
The discriminants associated to isotropy representations of symmetric spaces
Claudio Gorodski
Mathematics , 2010,
Abstract: We consider a generalized discriminant associated to a symmetric space which generalizes the discriminant of real symmetric matrices, and note that it can be written as a sum of squares of real polynomials. A method to estimate the minimum number of squares required to represent the discrimininant is developed and applied in examples.
Taut representations of compact simple Lie groups
Claudio Gorodski
Mathematics , 2004,
Abstract: In this paper we classify the reducible representations of compact simple Lie groups all of whose orbits are tautly embedded in Euclidean space with respect to Z_2 coefficients.
Singular riemannian foliations with sections, transnormal maps and basic forms
Marcos Alexandrino,Claudio Gorodski
Mathematics , 2006, DOI: 10.1007/s10455-006-9052-6
Abstract: A singular riemannian foliation F on a complete riemannian manifold M is said to admit sections if each regular point of M is contained in a complete totally geodesic immersed submanifold (a section) that meets every leaf of F orthogonally and whose dimension is the codimension of the regular leaves of F. We prove that the algebra of basic forms of M relative to F is isomorphic to the algebra of those differential forms on a section that are invariant under the generalized Weyl pseudogroup of this section. This extends a result of Michor for polar actions. It follows from this result that the algebra of basic function is finitely generated if the sections are compact. We also prove that the leaves of F coincide with the level sets of a transnormal map (generalization of isoparametric map) if M is simply connected, the sections are flat and the leaves of F are compact. This result extends previous results due to Carter and West, Terng, and Heintze, Liu and Olmos.
Polar orthogonal representations of real reductive algebraic groups
Laura Geatti,Claudio Gorodski
Mathematics , 2008,
Abstract: We prove that a polar orthogonal representation of a real reductive algebraic group has the same closed orbits as the isotropy representation of a pseudo-Riemannian symmetric space. We also develop a partial structural theory of polar orthogonal representations of real reductive algebraic groups which slightly generalizes some results of the structural theory of real reductive Lie algebras.
Representations whose minimal reduction has a toric identity component
Claudio Gorodski,Alexander Lytchak
Mathematics , 2012,
Abstract: We classify irreducible representations of connected compact Lie groups whose orbit space is isometric to the orbit space of a representation of a finite extension of (positive dimensional) toric group. They turn out to be exactly the non-polar irreducible representations preserving an isoparametric submanifold and acting with cohomogeneity one on it.
Isometric actions on spheres with an orbifold quotient
Claudio Gorodski,Alexander Lytchak
Mathematics , 2014,
Abstract: We classify representations of compact connected Lie groups whose induced action on the unit sphere has an orbit space isometric to a Riemannian orbifold.
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