A note on surfaces with prescribed oriented Euclidean Gauss map
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 t...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.537 |
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| _version_ | 1832559044659773440 |
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| author | Ricardo Sa Earp Eric Toubiana |
| author_facet | Ricardo Sa Earp Eric Toubiana |
| author_sort | Ricardo Sa Earp |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-f9859c94c6dc4109a292a06d5e39a4a8 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-f9859c94c6dc4109a292a06d5e39a4a82025-02-03T01:31:07ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005453754310.1155/IJMMS.2005.537A note on surfaces with prescribed oriented Euclidean Gauss mapRicardo Sa Earp0Eric Toubiana1Departamento de Matemática, Pontifícia Universidade Católica do Rio de Janeiro, Rua Marquâs de São Vicente, 225-Gávea, Rio de Janeiro, BrazilCentre de Mathématiques de Jussieu, Université Paris 7-Denis Diderot, 2 Place Jussieu, Paris Cedex 05 F-75251, FranceWe 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.http://dx.doi.org/10.1155/IJMMS.2005.537 |
| spellingShingle | Ricardo Sa Earp Eric Toubiana A note on surfaces with prescribed oriented Euclidean Gauss map International Journal of Mathematics and Mathematical Sciences |
| title | A note on surfaces with prescribed oriented Euclidean Gauss map |
| title_full | A note on surfaces with prescribed oriented Euclidean Gauss map |
| title_fullStr | A note on surfaces with prescribed oriented Euclidean Gauss map |
| title_full_unstemmed | A note on surfaces with prescribed oriented Euclidean Gauss map |
| title_short | A note on surfaces with prescribed oriented Euclidean Gauss map |
| title_sort | note on surfaces with prescribed oriented euclidean gauss map |
| url | http://dx.doi.org/10.1155/IJMMS.2005.537 |
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