Isometric deformations of the $ {\mathcal{K}}^{\frac{1}{4}}$-flow translators in $ {\mathbb{R}}^{3}$ with helicoidal symmetry

Lee, Hojoo

doi:10.1016/j.crma.2013.06.006

Differential Geometry

Isometric deformations of the

K^{\frac{1}{4}}

-flow translators in

R^{3}

with helicoidal symmetry
[Déformations isométriques des translateurs du flot

K^{1 / 4}

dans

R^{3}

à symétrie hélicoïdale]

Présenté par : the Editorial Board

Lee, Hojoo ¹

¹ Korea Institute for Advanced Study, 207-43 Cheongryangri 2-dong, Dongdaemun-gu, Seoul 130-722, Republic of Korea

Comptes Rendus. Mathématique, Tome 351 (2013) no. 11-12, pp. 477-482.

Résumé
Abstract

Les fonctions de hauteur des translateurs du flot $K^{1 / 4}$ de $R^{3}$ résolvent lʼéquation de Monge–Ampère classique $f_{x x} f_{y y} - f_{x y}^{2} = 1$ . Nous déterminons de manière géométrique explicite lʼespace des modules de tous les translateurs à symétrie hélicoïdale du flot $K^{1 / 4}$ , qui sont engendré à partir de courbes planes par lʼaction de groupes hélicoïdaux.

The height functions of $K^{\frac{1}{4}}$ -flow translators in the Euclidean space $R^{3}$ solve the classical Monge–Ampère equation $f_{x x} f_{y y} - f_{x y}^{2} = 1$ . We explicitly and geometrically determine the moduli space of all helicoidal $K^{\frac{1}{4}}$ -flow translators, which are generated from planar curves by the action of helicoidal groups.

Reçu le : 2012-07-04
Accepté le : 2013-06-19
Publié le : 2013-06-01

DOI : 10.1016/j.crma.2013.06.006

Affiliations des auteurs :

Lee, Hojoo ¹

¹ Korea Institute for Advanced Study, 207-43 Cheongryangri 2-dong, Dongdaemun-gu, Seoul 130-722, Republic of Korea

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     title = {Isometric deformations of the $ {\mathcal{K}}^{\frac{1}{4}}$-flow translators in $ {\mathbb{R}}^{3}$ with helicoidal symmetry},
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     pages = {477--482},
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Lee, Hojoo. Isometric deformations of the $ {\mathcal{K}}^{\frac{1}{4}}$-flow translators in $ {\mathbb{R}}^{3}$ with helicoidal symmetry. Comptes Rendus. Mathématique, Tome 351 (2013) no. 11-12, pp. 477-482. doi : 10.1016/j.crma.2013.06.006. http://www.numdam.org/articles/10.1016/j.crma.2013.06.006/

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Cité par Sources :

^☆ This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (Ministry of Education, Science and Technology) [NRF-2011-357-C00007].