A PDE for Smooth Isometric Immersion of an Open Set of the Hyperbolic Plane ℍ2 into ℝ4

Mor Dione
Bira Gaye Diop
Athoumane Niang

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Publication date

January 2021

DOI

10.1155/2021/2012354

Publisher

Hindawi Limited

Journal

Journal of Mathematics

Abstract

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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A PDE for Smooth Isometric Immersion of an Open Set of the Hyperbolic Plane ℍ2 into ℝ4

Abstract

Extracted data

A PDE for Smooth Isometric Immersion of an Open Set of the Hyperbolic Plane ℍ2 into ℝ4

Abstract

Extracted data

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