A PDE for smooth isometric immersion of an open set of the hyperbolic plane \(\mathbb{H}^2\) into \(\mathbb{R}^4\) (Q2051611)
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scientific article; zbMATH DE number 7433051
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A PDE for smooth isometric immersion of an open set of the hyperbolic plane \(\mathbb{H}^2\) into \(\mathbb{R}^4\) |
scientific article; zbMATH DE number 7433051 |
Statements
A PDE for smooth isometric immersion of an open set of the hyperbolic plane \(\mathbb{H}^2\) into \(\mathbb{R}^4\) (English)
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24 November 2021
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Summary: A simple interpretation of the PDE for isometric immersion of the hyperbolic plane \(\mathbb{H}^2\) into \(\mathbb{R}^4\) 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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