publication . Article . 2017

Пересечения полиномиальных линий с плоскостями

Поликанова, И.В.;
Open Access Russian
  • Published: 01 Nov 2017 Journal: Izvestiya of Altai State University (issn: 1561-9451, eissn: 1561-9443, Copyright policy)
  • Publisher: Izvestiya of Altai State University
Abstract
There are different approaches to determining such characteristics of a curve as osculating plane, flattening and its order. The difference in approaches is because the curves are considered in different spaces: affine and projective. Therefore, the wordings are given in terms of the relevant structures: for curves in affine space – through a linear dependence or independence of the vector systems, for curves in the projective space – through the intersection multiplicity of a curve and the planes. The interpenetration of the two points of view can be realized through the common to both spaces concept of intersection multiplicity of a curve and a surface or thro...

2. Uribe-Vargas R. On Vertices, Focal Curvatures and Differential Geometry of Spase Curves // Bull. Braz. Math. Soc., new series. 2005. T. 36(3).

5. Анисов С.С. Выпуклые кривые в RP n //Локальные и глобальные задачи теории особен- ностей: сб. ст. к 60-летию академика Владимира Игоревича Арнольда: труды МИАН 221. М., 1998.

6. Anisov C.C. Projective convex curves // The Arnold-Gelfand mothematical seminars: geometry and singularity theory. Boston, 1997.

7. Arnold V.I. On the number of flattening points on space curves // Amer. Math. Soc. Transl. (2) 1995. V. 171.

10. Uribe-Vargas R. On 4-flattening Theorems and the Curves of Charateodory, Barner and Segre // Journal of Geometry. 2003. Т. 77.

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