PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 39(53), pp. 169172 (1986) 

SOME GLOBAL PROPERTIES OF PLANE CURVESWaldemar Cie\'slakInstitut Matematyki UMCS Pl. M. Sklodowskiej 1, 20031 Lublin, PolandAbstract: 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 socalled $\nu$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 Full text of the article:
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