Search results for "Hyperplane"

showing 3 items of 23 documents

Geometric contacts of surfaces immersed in Rn, n⩾5

2009

Abstract We study the extrinsic geometry of surfaces immersed in R n , n ⩾ 5 , by analyzing their contacts with different standard geometrical models, such as hyperplanes and hyperspheres. We investigate the relation between different types of contact and the properties of the curvature ellipses at each point. In particular, we focalize our attention on the hyperspheres having contacts of corank two with the surface. This leads in a natural way to the concept of umbilical focus and umbilic curvature.

Surface (mathematics)Computational Theory and MathematicsHyperplaneMathematical analysisPoint (geometry)GeometryMathematics::Differential GeometryGeometry and TopologyCurvatureEllipseFocus (optics)AnalysisMathematicsDifferential Geometry and its Applications
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A note on the Lawrence-Krammer-Bigelow representation

2002

A very popular problem on braid groups has recently been solved by Bigelow and Krammer, namely, they have found a faithful linear representation for the braid group B_n. In their papers, Bigelow and Krammer suggested that their representation is the monodromy representation of a certain fibration. Our goal in this paper is to understand this monodromy representation using standard tools from the theory of hyperplane arrangements. In particular, we prove that the representation of Bigelow and Krammer is a sub-representation of the monodromy representation which we consider, but that it cannot be the whole representation.

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Pure mathematicsLinear representation[ MATH.MATH-GR ] Mathematics [math]/Group Theory [math.GR]Braid group20F36Group Theory (math.GR)52C3001 natural sciences[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]52C35Mathematics - Geometric TopologyMathematics::Group TheoryMathematics::Algebraic Geometry[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciencesFOS: Mathematics20F36 52C35 52C30 32S22braid groups0101 mathematicsMathematics::Representation TheoryComputingMilieux_MISCELLANEOUSMathematics[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT][MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]linear representations010102 general mathematicsRepresentation (systemics)FibrationSalvetti complexesGeometric Topology (math.GT)Mathematics::Geometric TopologyHyperplaneMonodromy010307 mathematical physicsGeometry and TopologyMathematics - Group Theory32S22
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Splines in convex sets under constraints of two‐sided inequality type in a hyperplane

2008

The problem of minimization of a smoothing functional under inequality constraints is considered in a hyperplane. The conditions of the existence of a solution are obtained and some properties of this solution are investigated. It is proved that the solution is a spline. The method for its construction is suggested. First Published Online: 14 Oct 2010

smoothing problemMathematical analysisRegular polygonLinear matrix inequalityHalf-spacesplineSpline (mathematics)Simplex algorithmHyperplaneModeling and SimulationQA1-939Applied mathematicsThin plate splinesimplex methodAnalysisSmoothingMathematicsMathematicsMathematical Modelling and Analysis
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