Proceedings of the International Conference on Geometry, Integrability and Quantization

News on Immersions of the Lobachevsky Space into Euclidean Space

Yurij Aminov

Abstract

An exposition of the new results concerning the nonexistence of local isometric immersions of 3-dimensional Lobachevsky space $L^3$ into 5-dimensional Euclidean space $E^5$ with constant curvature of the Grassmannian image metric, on connections between curvatures of asymptotic lines on a domain of $L^3 \subset E^5$, on regularity theorems for surfaces obtained by Backlund transformation of a domain of $L^2 \subset S^3$ and $L^2 \subset E^3$.

Article information

Source
Proceedings of the Third International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov and Gregory L. Naber, eds. (Sofia: Coral Press Scientific Publishing, 2002), 165-170

Dates
First available in Project Euclid: 12 June 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1434145465

Digital Object Identifier
doi:doi:10.7546/giq-3-2002-165-170

Mathematical Reviews number (MathSciNet)
MR1884843

Zentralblatt MATH identifier
1022.53049

Citation

Aminov, Yurij. News on Immersions of the Lobachevsky Space into Euclidean Space. Proceedings of the Third International Conference on Geometry, Integrability and Quantization, 165--170, Coral Press Scientific Publishing, Sofia, Bulgaria, 2002. doi:doi:10.7546/giq-3-2002-165-170. https://projecteuclid.org/euclid.pgiq/1434145465


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