Osculating quadric of the spatial curve

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

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.).
Published
2017-12-02
Keywords: space curve, osculating sphere, osculating quadric
How to Cite
Lysenko, V. V., & Timokhovich, V. L. (2017). Osculating quadric of the spatial curve. Journal of the Belarusian State University. Mathematics and Informatics, 1, 10-15. Retrieved from https://journals.bsu.by/index.php/mathematics/article/view/731
Issue
No 1 (2017): Journal of the Belarusian State University. Mathematics and Informatics
Section
Geometry and Topology

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