Search results for "Differential geometry of curves"

showing 2 items of 2 documents

Salkowski curves revisited: A family of curves with constant curvature and non-constant torsion

2009

In the paper [Salkowski, E., 1909. Zur Transformation von Raumkurven, Mathematische Annalen 66 (4), 517-557] published one century ago, a family of curves with constant curvature but non-constant torsion was defined. We characterize them as space curves with constant curvature and whose normal vector makes a constant angle with a fixed line. The relation between these curves and rational curves with double Pythagorean hodograph is studied. A method to construct closed curves, including knotted curves, of constant curvature and continuous torsion using pieces of Salkowski curves is outlined.

Mathematical analysisAerospace EngineeringDifferential geometry of curvesCurvatureComputer Graphics and Computer-Aided DesignConstant curvatureParametric surfaceModeling and SimulationFundamental theorem of curvesTorsion of a curveAutomotive EngineeringFamily of curvesConstant (mathematics)MathematicsComputer Aided Geometric Design
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Differential Geometry of Curves and Surfaces

2001

The goal of this article is to present the relation between some differential formulas, like the Gauss integral for a link, or the integral of the Gaussian curvature on a surface, and topological invariants like the linking number or the Euler characteristic.

PhysicsSurface (mathematics)symbols.namesakeFrenet–Serret formulasGaussian integralMathematical analysisGaussian curvaturesymbolsConstant-mean-curvature surfaceDifferential geometry of curvesLinking numberDifferential (mathematics)
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