International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 4, Pages 537-543
doi:10.1155/IJMMS.2005.537
A note on surfaces with prescribed oriented Euclidean Gauss map
Ricardo Sa Earp1
and Eric Toubiana2
1Departamento de Matemática, Pontifícia Universidade Católica do Rio de Janeiro, Rua Marquâs de São Vicente, 225-Gávea, Rio de Janeiro, Brazil
2Centre de Mathématiques de Jussieu, Université Paris 7-Denis Diderot, 2 Place Jussieu, Paris Cedex 05 F-75251, France
Abstract
We present another proof of a theorem due to Hoffman and Osserman in Euclidean space concerning the determination of a conformal immersion by its Gauss map. Our approach depends on geometric quantities, that is, the hyperbolic Gauss map G and formulae obtained in hyperbolic space. We use the idea that the Euclidean Gauss map and the hyperbolic Gauss map with some compatibility relation determine a conformal immersion, proved in a previous paper.