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Curves

  • Anatolij T. Fomenko
  • Tosiyasu L. Kinii

Abstract

We consider Euclidean space ℝn and define in it the standard Euclidean scalar product
$$\langle \xi ,\eta \rangle = {\xi ^1}{\eta ^1} + \cdots + {\xi ^n}{\eta ^n}$$
for any vectors ξ and η. With each vector ξ we associate a real number, called its length and defined as
$$\left| \xi \right| = {\left\langle {\xi ,\xi } \right\rangle ^{\frac{1}{2}}}$$

Keywords

Jacobian Matrix Smooth Curve Rigid Motion Plane Curf Polar Coordinate System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Japan 1997

Authors and Affiliations

  • Anatolij T. Fomenko
    • 1
  • Tosiyasu L. Kinii
    • 2
    • 3
  1. 1.Department of Differential Geometry and Application, Faculty of Mathematics and MechanicsMoscow State UniversityMoscowRussia
  2. 2.Laboratory of Digital Art and TechnologyTokyo, 113Japan
  3. 3.Senior Partner of MONOLITH Co. LtdTokyo, 106Japan

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