Osculating quadric of the spatial curve

Authors

  • Valery V. Lysenko Belarusian State University, Nezavisimosti avenue, 4, 220030, Minsk
  • Vladimir L. Timokhovich Belarusian State University, Nezavisimosti avenue, 4, 220030, Minsk

Keywords:

space curve, osculating sphere, osculating quadric

Abstract

In the investigation of local properties of a space curve assotiated objects which have good approximation characteristics are often used. The main ones – the osculating plane and the osculating sphere. As known, the osculating plane has tangency of at least 2nd degree with the curve, while the osculating sphere – at least 3rd degree. In the paper a problem of finding of 2nd degree surface (the osculating quadric) which has tangency of at least 6th degree is considered. It is proved the osculating quadric exists and a method of its construction is described. Also existence of osculating quadric of any basic type of 2nd degree surface is pointed out.

Author Biography

  • Valery V. Lysenko, Belarusian State University, Nezavisimosti avenue, 4, 220030, Minsk

    student at the faculty of mechanics and mathematics

References

  1. Vygodsky M. Y. Differentsialʼnaya geometriya [Differential geometry]. Moscow ; Leningrad, 1949 (in Russ.).
  2. Finikov S. P. Kurs differentsialʼnoi geometrii [Course of differential geometry]. Moscow, 1952 (in Russ.).

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Published

2017-12-02

Issue

No. 1 (2017): Journal of the Belarusian State University. Mathematics and Informatics

Section

Geometry and Topology

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How to Cite

[1]
Lysenko, V.V. and Timokhovich, V.L. 2017. Osculating quadric of the spatial curve. Journal of the Belarusian State University. Mathematics and Informatics. 1 (Dec. 2017), 10–15.