Search results for "Hyperbolic triangle"

showing 4 items of 4 documents

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
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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
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The horospherical Gauss-Bonnet type theorem in hyperbolic space

2006

We introduce the notion horospherical curvatures of hypersurfaces in hyperbolic space and show that totally umbilic hypersurfaces with vanishing cur- vatures are only horospheres. We also show that the Gauss-Bonnet type theorem holds for the horospherical Gauss-Kronecker curvature of a closed orientable even dimensional hypersurface in hyperbolic space. + (i1) by using the model in Minkowski space. We introduced the notion of hyperbolic Gauss indicatrices slightly modified the definition of hyperbolic Gauss maps. The notion of hyperbolic indicatrices is independent of the choice of the model of hyperbolic space. Using the hyperbolic Gauss indicatrix, we defined the principal hyperbolic curv…

Pure mathematicsMathematics::Dynamical SystemsGauss-Bonnet type theoremHyperbolic groupMathematics::Complex VariablesGeneral MathematicsHyperbolic spaceMathematical analysisHyperbolic manifoldUltraparallel theoremhorospherical geometryhyperbolic Gauss mapshypersurfacesRelatively hyperbolic groupMathematics::Geometric Topology53A3553A0558C27hyperbolic spaceHyperbolic angleMathematics::Differential GeometryMathematics::Representation TheoryHyperbolic triangleHyperbolic equilibrium pointMathematics
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On bounds for total absolute curvature of surfaces in hyperbolic 3-space

2003

Abstract We construct examples of surfaces in hyperbolic space which do not satisfy the Chern–Lashof inequality (which holds for immersed surfaces in Euclidean space). To cite this article: R. Langevin, G. Solanes, C. R. Acad. Sci. Paris, Ser. I 336 (2003).

Surface (mathematics)Differential geometryEuclidean spaceHyperbolic spaceMathematical analysisHyperbolic manifoldTotal curvatureGeneral MedicineCurvatureHyperbolic triangleMathematicsComptes Rendus Mathematique
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