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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Autores principales:	Mor Dione, Bira Gaye Diop, Athoumane Niang
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/3afcfc69b22c4a4bb8705a331e5cbd17
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spelling	oai:doaj.org-article:3afcfc69b22c4a4bb8705a331e5cbd172021-11-08T02:37:08ZA PDE for Smooth Isometric Immersion of an Open Set of the Hyperbolic Plane ℍ2 into ℝ42314-478510.1155/2021/2012354https://doaj.org/article/3afcfc69b22c4a4bb8705a331e5cbd172021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/2012354https://doaj.org/toc/2314-4785A 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.Mor DioneBira Gaye DiopAthoumane NiangHindawi LimitedarticleMathematicsQA1-939ENJournal of Mathematics, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Mor Dione Bira Gaye Diop Athoumane Niang A PDE for Smooth Isometric Immersion of an Open Set of the Hyperbolic Plane ℍ2 into ℝ4
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
author	Mor Dione Bira Gaye Diop Athoumane Niang
author_facet	Mor Dione Bira Gaye Diop Athoumane Niang
author_sort	Mor Dione
title	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_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_sort	pde for smooth isometric immersion of an open set of the hyperbolic plane ℍ2 into ℝ4
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/3afcfc69b22c4a4bb8705a331e5cbd17
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A PDE for Smooth Isometric Immersion of an Open Set of the Hyperbolic Plane ℍ2 into ℝ4

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