Search results for "Hyperbolic 3-manifold"

showing 7 items of 7 documents

On the hyperbolic limit points of groups acting on hyperbolic spaces

1998

We study the hyperbolic limit points of a groupG acting on a hyperbolic metric space, and consider the question of whether any attractive limit point corresponds to a unique repulsive limit point. In the special case whereG is a (non-elementary) finitely generated hyperbolic group acting on its Cayley graph, the answer is affirmative, and the resulting mapg +↦g −, is discontinuous everywhere on the hyperbolic boundary. We also provide a direct, combinatorial proof in the special case whereG is a (non-abelian) free group of finite type, by characterizing algebraically the hyperbolic ends ofG.

Discrete mathematicsPure mathematicsHyperbolic groupGeneral MathematicsHyperbolic 3-manifoldHyperbolic angleHyperbolic manifoldUltraparallel theoremRelatively hyperbolic groupMathematicsHyperbolic equilibrium pointHyperbolic treeRendiconti del Circolo Matematico di Palermo
researchProduct

Total curvatures of convex hypersurfaces in hyperbolic space

1999

We give sharp upper estimates for the difference circumradius minus inradius and for the angle between the radial vector (respect to the center of an inball) and the normal to the boundary of a compact $h$-convex domain in the hyperpolic space. We apply these estimates to get the limit at the infinity for the quotients Volume/Area and (Total $k$-mean curvature)/Area of a family of $h$-convex domains which expand over the whole space. The theorem for the first quotient gives an extension to arbitrary dimension of a result of Santalo and Yanez for the hyperbolic plane.

Hyperbolic groupGeneral MathematicsHyperbolic spaceHyperbolic 3-manifoldMathematical analysisHyperbolic angleMathematics::Metric GeometryHyperbolic manifoldUltraparallel theoremHyperbolic triangleRelatively hyperbolic groupMathematicsIllinois Journal of Mathematics
researchProduct

THE HOROSPHERICAL GEOMETRY OF SUBMANIFOLDS IN HYPERBOLIC SPACE

2005

Some geometrical properties associated to the contact of submanifolds with hyperhorospheres in hyperbolic -space are studied as an application of the theory of Legendrian singularities.

Hyperbolic groupGeneral MathematicsHyperbolic spaceMathematical analysisHyperbolic 3-manifoldHyperbolic manifoldUltraparallel theoremGeometryHyperbolic motionMathematics::Geometric TopologyRelatively hyperbolic groupMathematics::Differential GeometryMathematics::Symplectic GeometryHyperbolic triangleMathematicsJournal of the London Mathematical Society
researchProduct

Non-equivalent hyperbolic knots

2002

We construct, for each integer n 3, pairs of non-equivalent hyperbolic knots with the same 2fold and n-fold cyclic branched covers. We also discuss necessary conditions for such pairs of knots to exist.  2001 Elsevier Science B.V. All rights reserved. MSC: primary 57M25; secondary 57M12, 57M50

Hyperbolic knotsPure mathematicsQuantitative Biology::BiomoleculesCyclic branched coversHyperbolic groupSkein relationHyperbolic 3-manifoldOrbifoldsHyperbolic manifoldVolume conjectureMathematics::Geometric TopologyBonahon–Siebenmann decompositionKnot theoryAlgebraIntegerGeometry and TopologyMathematicsTopology and its Applications
researchProduct

Non-immersion theorem for a class of hyperbolic manifolds

1998

Abstract It is proved that a non-simply-connected complete hyperbolic manifold cannot be isometrically immersed in a Euclidean space with a flat normal connection. In particular, the complete hyperbolic manifold M n with π 1 ( M ) ≠ 0 cannot be isometrically immersed in R 2 n − 1 .

Pure mathematicsHyperbolic groupHyperbolic spaceMathematical analysisHyperbolic 3-manifoldHyperbolic manifoldUltraparallel theoremMathematics::Geometric TopologyRelatively hyperbolic groupStable manifoldComputational Theory and MathematicsMathematics::Metric GeometryMathematics::Differential GeometryGeometry and TopologyAnalysisHyperbolic equilibrium pointMathematicsDifferential Geometry and its Applications
researchProduct

Hyperbolic isometries versus symmetries of links

2009

We prove that every finite group is the orientation-preserving isometry group of the complement of a hyperbolic link in the 3-sphere.

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Pure mathematicsHyperbolic groupHyperbolic linkTotally geodesic surfaces01 natural sciencesRelatively hyperbolic group57M60Mathematics - Geometric Topology[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciencesFOS: Mathematics0101 mathematicsMathematics[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]Hyperbolic linksHyperbolic space010102 general mathematicsHyperbolic 3-manifoldHyperbolic manifoldGeometric Topology (math.GT)Algebra010307 mathematical physicsGeometry and TopologyIsometry groupHyperbolic Dehn surgeryHyperbolic Dehn surgeryTopology and its Applications
researchProduct

Conway irreducible hyperbolic knots with two common covers

2005

International audience; For each pair of coprime integers n > m ≥ 2 we construct pairs of non equivalent Conway irreducible hyperbolic knots with the same n-fold and m-fold cyclic branched covers.

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Pure mathematicsQuantitative Biology::BiomoleculesCoprime integersHyperbolic groupMathematics::Number TheoryGeneral Mathematics010102 general mathematicsSkein relationHyperbolic 3-manifoldVolume conjecture01 natural sciencesRelatively hyperbolic groupMathematics::Geometric TopologyKnot theoryAlgebra[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciences010307 mathematical physics0101 mathematicsMathematics[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]
researchProduct