On Isometric Immersions of the Lobachevsky Plane into 4-Dimensional Euclidean Space with Flat Normal Connection
According to Hilbert's theorem, the Lobachevsky plane $L^2$ does not admit a regular isometric immersion into $E^3$. The question on the existence of isometric immersion of $L^2$ into $E^4$ remains open. We consider isometric immersions into $E^4$ with flat normal connection and find a fundame...
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| Datum: | 2020 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2020
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| Online Zugang: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/jm16-0208e |
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| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
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Journal of Mathematical Physics, Analysis, Geometry| Zusammenfassung: | According to Hilbert's theorem, the Lobachevsky plane $L^2$ does not admit a regular isometric immersion into $E^3$. The question on the existence of isometric immersion of $L^2$ into $E^4$ remains open. We consider isometric immersions into $E^4$ with flat normal connection and find a fundamental system of two
partial differential equations of the second order for two functions. We prove the theorems on the non-existence of global and local isometric immersions for the case under consideration.
Mathematics Subject Classification: 53C23, 53C45 |
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