×

Isometric immersions of the Lobachevskij plane in \(E^ 4\). (English. Russian original) Zbl 0697.53014

Sib. Math. J. 30, No. 5, 805-811 (1989); translation from Sib. Mat. Zh. 30, No. 5(177), 179-186 (1989).
The author proves that the Lobachevsky plane admits an isometric immersion into a 4-dimensional Euclidean space as a generalized \(C^{0,1}\)-surface of rotation, but there is no generalized \(C^ 1\)- surface of rotation which is isometric to the Lobachevsky plane.
Reviewer: V.T.Fomenko

MSC:

53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces
53B20 Local Riemannian geometry
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] G. Blanu?a, Über die Einbettung hyperbolischer Räume in euklidische Räume,? Monatshefte Mathematik,59, No. 3, 217-229 (1955). · Zbl 0067.14403 · doi:10.1007/BF01303796
[2] É. R. Rozendorn, ?Realization of the metric ds2=du2+f(u)dv2 in five-dimensional Euclidean space,? Dokl. Akad. Nauk ArmSSR,30, No. 4, 197-199 (1960).
[3] S. B. Kadomtsev, ?Impossility of some special isometric immersions of Lobachevskii space,? Mat. Sb.,107, No. 2, 175-198 (1978).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.