Geodesic
Some Global Properties of Plane Curves
Publications de l'Institut Mathématique, _N_S_39 (1986) no. 53, p. 169
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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 : 53C65 
@article{PIM_1986_N_S_39_53_a23,
     author = {Waldemar Cie\'slak},
     title = {Some {Global} {Properties} of {Plane} {Curves}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {169 },
     year = {1986},
     volume = {_N_S_39},
     number = {53},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1986_N_S_39_53_a23/}
}
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Waldemar Cieślak. Some Global Properties of Plane Curves. Publications de l'Institut Mathématique, _N_S_39 (1986) no. 53, p. 169 . http://geodesic.mathdoc.fr/item/PIM_1986_N_S_39_53_a23/