Isometric immersions of a Euclidean plane in Lobachevskii space

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1971 English Publisher:Springer Science and Business Media LLCJournal:Mathematical Notes of the Academy of Sciences of the USSR, volume 10, pages 619-622 (issn: 0001-4346, eissn: 1573-8876,

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Authors: Volkov, Yu. A.; Vladimirova, S. M.;

doi: 10.1007/bf01464724

Isometric immersions of a Euclidean plane in Lobachevskii space

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Abstract

It is proved that any regular isometric immersion of a Euclidean plane in (three-dimensional) Lobachevskii space is either a homeomorphism onto an orisphere or a covering of the surface formed by the rotation of an equidistant about its base.

Related Organizations

St Petersburg University
Russian Federation

Keywords

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.), Global surface theory (convex surfaces à la A. D. Aleksandrov)

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