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This paper develops in detail the dierential geometryof ruled surfaces from two perspectives, and presents the under-lying relations which unite them. Both scalar and dual curvaturefunctions which dene the shape of a ruled surface are derived.Explicit formulas are presented for the computation of these func-tions in both formulations of the dierential geometry of ruled sur-faces. Also presented is a detailed analysis of the ruled surface whichcharacterizes the shape of a general ruled surface in the same waythat osculating circle characterizes locally the shape of a non-nullLorentzian curve.
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참고문헌 (9)
참고문헌 신청
/ 1976 / On the use of dual numbers vectors and matrices in instan-taneous
/ 1981 / The Curvature Theory of Line Trajectories inSpatial Kinematics ASME Journal of Mechanical Design 103
/ 1983 / Semi-Riemannian Geometry with Applications to Relativity Scalar and dual formulations of the curvature theory 1355
/ 1984 / Trigonometry in Lorentzian Geometry (mizu)
/ 1987 / On the Scalar and Dual Formulations of the Curvature Theoryof Line Trajectories Journal of Mechanisms
/ 1981 / The Curvature Theory of Line Trajectories inSpatial Kinematics ASME Journal of Mechanical Design 103
/ 1983 / Semi-Riemannian Geometry with Applications to Relativity Scalar and dual formulations of the curvature theory 1355
/ 1984 / Trigonometry in Lorentzian Geometry (mizu)
/ 1987 / On the Scalar and Dual Formulations of the Curvature Theoryof Line Trajectories Journal of Mechanisms
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