Geodesic
Osculating quadric of the spatial curve
Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2017), pp. 11-15
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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 $2^{nd}$ degree with the curve, while the osculating sphere – at least $3^{rd}$ degree. In the paper a problem of finding of $2^{nd}$ degree surface (the osculating quadric) which has tangency of at least $6^{th}$ 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 $2^{nd}$ degree surface is pointed out.
Keywords: space curve; osculating sphere; osculating quadric. 
@article{BGUMI_2017_1_a1,
     author = {V. Lysenko and V. L. Timokhovich},
     title = {Osculating quadric of the spatial curve},
     journal = {Journal of the Belarusian State University. Mathematics and Informatics},
     pages = {11--15},
     year = {2017},
     volume = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/BGUMI_2017_1_a1/}
}
TY  - JOUR
AU  - V. Lysenko
AU  - V. L. Timokhovich
TI  - Osculating quadric of the spatial curve
JO  - Journal of the Belarusian State University. Mathematics and Informatics
PY  - 2017
SP  - 11
EP  - 15
VL  - 1
UR  - http://geodesic.mathdoc.fr/item/BGUMI_2017_1_a1/
LA  - ru
ID  - BGUMI_2017_1_a1
ER  - 
%0 Journal Article
%A V. Lysenko
%A V. L. Timokhovich
%T Osculating quadric of the spatial curve
%J Journal of the Belarusian State University. Mathematics and Informatics
%D 2017
%P 11-15
%V 1
%U http://geodesic.mathdoc.fr/item/BGUMI_2017_1_a1/
%G ru
%F BGUMI_2017_1_a1
V. Lysenko; V. L. Timokhovich. Osculating quadric of the spatial curve. Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2017), pp. 11-15. http://geodesic.mathdoc.fr/item/BGUMI_2017_1_a1/

[1] M. Ya. Vygodskii, “Differentsialnaya geometriya”, 1949

[2] S. P. Finikov, “Kurs differentsialnoi geometrii”, 1952