A note on surfaces with prescribed oriented Euclidean Gauss map | Zendy

Ricardo Sá Earp | Zendy; Éric Toubiana | Zendy

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A note on surfaces with prescribed oriented Euclidean Gauss map

Author(s) -

Ricardo Sá Earp,

Éric Toubiana

Publication year - 2005

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/ijmms.2005.537

Subject(s) - gauss map , mathematics , gauss , conformal map , hyperbolic space , euclidean geometry , immersion (mathematics) , euclidean space , quadratic gauss sum , mathematical analysis , hyperbolic geometry , pure mathematics , euclidean distance , geometry , differential geometry , physics , quantum mechanics

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

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