A note on surfaces with prescribed oriented Euclidean Gauss map

Ricardo Sa Earp and Eric Toubiana

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-7

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.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:647814

DOI: 10.1155/IJMMS.2005.537

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