no. 23-24
Geometry/Differential Geometry
A congruence theorem for minimal surfaces in S5 with constant contact angle
[Théorème de congruence pour les surfaces minimales en S5 avec angle de contact constant]

Présenté par : Étienne Ghys

Montes, Rodrigo Ristow1
1 Departamento de Matemática, Universidade Federal da Paraíba, BR-58.051-900, João Pessoa, P.B., Brazil
Comptes Rendus. Mathématique, Tome 346 (2008) no. 23-24, pp. 1275-1278.

Nous présentons un théorème de congruence pour les surfaces minimales en S5 avec angle de contact constant en utilisant les équations de Gauss–Codazzi–Ricci. Plus précisémént, nous prouvons que les équations de Gauss–Codazzi–Ricci pour les surfaces minimales en S5 avec angle de contact constant satisfont une équation pour le Laplacien de l'angle holomorphe.

We provide a congruence theorem for minimal surfaces in S5 with constant contact angle using the Gauss–Codazzi–Ricci equations. More precisely, we prove that the Gauss–Codazzi–Ricci equations for minimal surfaces in S5 with constant contact angle satisfy an equation for the Laplacian of the holomorphic angle.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.10.013
Montes, Rodrigo Ristow 1

1 Departamento de Matemática, Universidade Federal da Paraíba, BR-58.051-900, João Pessoa, P.B., Brazil 
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     title = {A congruence theorem for minimal surfaces in $ {S}^{5}$ with constant contact angle},
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     pages = {1275--1278},
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Montes, Rodrigo Ristow. A congruence theorem for minimal surfaces in $ {S}^{5}$ with constant contact angle. Comptes Rendus. Mathématique, Tome 346 (2008) no. 23-24, pp. 1275-1278. doi : 10.1016/j.crma.2008.10.013. http://www.numdam.org/articles/10.1016/j.crma.2008.10.013/

[1] Aebischer, B. Sympletic Geometry, Progress in Mathematics, vol. 124, Springer-Verlag, Berlin–New York, 1992

[2] Chern, S.S.; Wolfson, J.G. Minimal surfaces by moving frames, Amer. J. Math., Volume 105 (1983), pp. 59-83

[3] Kenmotsu, K. On a parametrization of minimal immersions R2 into S5, Tohoku Math. J., Volume 27 (1975), pp. 83-90

[4] Montes, R.R.; Verderesi, J.A. Contact angle for immersed surfaces in S2n+1, Differential Geom. Appl., Volume 25 (2007), pp. 92-100

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