On the special parabolic points and the topology of the parabolic curve of certain smooth surfaces in 3
Comptes Rendus. Mathématique, Volume 334 (2002) no. 6, pp. 473-478.

In this Note we give a class of real polynomials of degree n⩾3 in two variables such that the parabolic curves of theirs graphs have at least (n−1)(n−2)/2 connected components diffeomorphic to the circle and exactly n(n−2) special parabolic points. These polynomials are of the form f=l1ln where li, i=1,…,n, are generic real affine functions on the plane.

Dans ce travail on donne une classe des polynômes réels de degré n⩾3 à deux variables tels que les courbes paraboliques de leurs graphes contiennent au moins (n−1)(n−2)/2 composantes connexes difféomorphes au cercle et exactement n(n−2) points paraboliques spéciaux. Ces polynômes sont de la forme f=l1ln où les li, i=1,…,n, sont des fonctions réelles affines génériques sur le plan.

Received:
Accepted:
Published online:
DOI: 10.1016/S1631-073X(02)02287-2
Ortiz-Rodríguez, Adriana 1

1 Équipe géométrie et dynamique, Université Paris 7, UFR de Math., case 7012, 175, rue du Chevaleret, 75013 Paris, France
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Ortiz-Rodríguez, Adriana. On the special parabolic points and the topology of the parabolic curve of certain smooth surfaces in $ \mathbb{R}^{3}$. Comptes Rendus. Mathématique, Volume 334 (2002) no. 6, pp. 473-478. doi : 10.1016/S1631-073X(02)02287-2. http://www.numdam.org/articles/10.1016/S1631-073X(02)02287-2/

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