A PDE for Smooth Isometric Immersion of an Open Set of the Hyperbolic Plane ℍ2 into ℝ4
A simple interpretation of the PDE for isometric immersion of the hyperbolic plane ℍ2 into ℝ4 is given. Thus, necessary and sufficient conditions are obtained. And, under natural additional conditions, we show that there are no complete solutions, but we can have special local solutions.
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/2012354 |
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| _version_ | 1832547769196216320 |
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| author | Mor Dione Bira Gaye Diop Athoumane Niang |
| author_facet | Mor Dione Bira Gaye Diop Athoumane Niang |
| author_sort | Mor Dione |
| collection | DOAJ |
| description | A simple interpretation of the PDE for isometric immersion of the hyperbolic plane ℍ2 into ℝ4 is given. Thus, necessary and sufficient conditions are obtained. And, under natural additional conditions, we show that there are no complete solutions, but we can have special local solutions. |
| format | Article |
| id | doaj-art-3afcfc69b22c4a4bb8705a331e5cbd17 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-3afcfc69b22c4a4bb8705a331e5cbd172025-02-03T06:43:31ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/2012354A PDE for Smooth Isometric Immersion of an Open Set of the Hyperbolic Plane ℍ2 into ℝ4Mor Dione0Bira Gaye Diop1Athoumane Niang2Cheikh Anta Diop UniversityCheikh Anta Diop UniversityCheikh Anta Diop UniversityA simple interpretation of the PDE for isometric immersion of the hyperbolic plane ℍ2 into ℝ4 is given. Thus, necessary and sufficient conditions are obtained. And, under natural additional conditions, we show that there are no complete solutions, but we can have special local solutions.http://dx.doi.org/10.1155/2021/2012354 |
| spellingShingle | Mor Dione Bira Gaye Diop Athoumane Niang A PDE for Smooth Isometric Immersion of an Open Set of the Hyperbolic Plane ℍ2 into ℝ4 Journal of Mathematics |
| title | A PDE for Smooth Isometric Immersion of an Open Set of the Hyperbolic Plane ℍ2 into ℝ4 |
| title_full | A PDE for Smooth Isometric Immersion of an Open Set of the Hyperbolic Plane ℍ2 into ℝ4 |
| title_fullStr | A PDE for Smooth Isometric Immersion of an Open Set of the Hyperbolic Plane ℍ2 into ℝ4 |
| title_full_unstemmed | A PDE for Smooth Isometric Immersion of an Open Set of the Hyperbolic Plane ℍ2 into ℝ4 |
| title_short | A PDE for Smooth Isometric Immersion of an Open Set of the Hyperbolic Plane ℍ2 into ℝ4 |
| title_sort | pde for smooth isometric immersion of an open set of the hyperbolic plane h2 into r4 |
| url | http://dx.doi.org/10.1155/2021/2012354 |
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