EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 39(53), pp. 169--172 (1986)

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SOME GLOBAL PROPERTIES OF PLANE CURVES

Waldemar Cie\'slak

Institut Matematyki UMCS Pl. M. Sklodowskiej 1, 20031 Lublin, Poland

Abstract: We introduce $L$-involutions for any positive number $L$ and we give a characterization of the class $(L)$ of all $L$-involutions. Then we define so-called $\nu$-involutive pairs of points of a curve $C\in \Cal M$ where $\Cal M$ is the family of all $C^1$ plane closed curves. For arbitrary $C\in \Cal M$ of length $L$ and for arbitrary $\nu\in (L)$ there exists a $\nu$-involutive pair of $C$ such that the tangent lines at the points ot this pair are parallel. Applications of this fact are given.

Classification (MSC2000): 53C65

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Electronic fulltext finalized on: 2 Nov 2001. This page was last modified: 16 Nov 2001.

© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
© 2001 ELibM for the EMIS Electronic Edition