Geodesic
On isometric immersions of the Lobachevsky plane into 4-dimensional Euclidean space with flat normal connection
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 16 (2020) no. 3, pp. 208-220 
Yuriy Aminov. On isometric immersions of the Lobachevsky plane into 4-dimensional Euclidean space with flat normal connection. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 16 (2020) no. 3, pp. 208-220. http://geodesic.mathdoc.fr/item/JMAG_2020_16_3_a0/
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     title = {On isometric immersions of the {Lobachevsky} plane into 4-dimensional {Euclidean} space with flat normal connection},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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