Search results for "Totally geodesic"

showing 3 items of 3 documents

Prescribing the behaviour of geodesics in negative curvature

2010

Given a family of (almost) disjoint strictly convex subsets of a complete negatively curved Riemannian manifold M, such as balls, horoballs, tubular neighborhoods of totally geodesic submanifolds, etc, the aim of this paper is to construct geodesic rays or lines in M which have exactly once an exactly prescribed (big enough) penetration in one of them, and otherwise avoid (or do not enter too much in) them. Several applications are given, including a definite improvement of the unclouding problem of [PP1], the prescription of heights of geodesic lines in a finite volume such M, or of spiraling times around a closed geodesic in a closed such M. We also prove that the Hall ray phenomenon desc…

Mathematics - Differential GeometryhoroballsPure mathematicsGeodesicDisjoint setsLagrange spectrum52A5501 natural sciences53C22Mathematics - Metric Geometry0103 physical sciences0101 mathematicshoroball[MATH.MATH-MG]Mathematics [math]/Metric Geometry [math.MG]MathematicsFinite volume methodHall rayAMS : 53 C 22 11 J 06 52 A 55 53 D 25Mathematics - Number Theory010102 general mathematicsnegative curvatureRiemannian manifold[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]Closed geodesic53D25[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]Totally geodesic010307 mathematical physicsGeometry and TopologyNegative curvatureMathematics::Differential GeometryConvex functiongeodesicgeodesics11J06
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The volume of geodesic balls and tubes about totally geodesic submanifolds in compact symmetric spaces

1997

AbstractLet M be a compact Riemannian symmetric space. We give an analytical expression for the area and volume functions of geodesic balls in M and for the area and volume functions of tubes around some totally geodesic submanifolds P of M. We plot the graphs of these functions for some compact irreducible Riemannian symmetric spaces of rank two.

Pure mathematicsGeodesictube53C21.Mathematical analysisGeodesic mapgeodesic balltotally geodesic submanifold.53C35Computational Theory and MathematicsSymmetric spaceTotally geodesicMathematics::Differential GeometryGeometry and TopologyCompact Riemannian symmetric spaceminimal focal distancerestricted rootsExponential map (Riemannian geometry)injectivity radiusAnalysisMathematicsDifferential Geometry and its Applications
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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
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