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On the existence of solutions of the system of Peterson–Codazzi and gauss equations
E. V. Shikin M. V. Lomonosov Moscow State University
Abstract:
This paper is concerned with isometric embeddings of complete two-dimensional metrics, defined on the plane, whose curvature is bounded by negative constants (metrics of type L). It is proved that under certain conditions any horocycle in a metric of type L (an analog of a horocycle in the Lobachevskii plane) admits a $C^3$-isometric embedding into $E^3$. The proof is based on the construction of a smooth solution of the system of Peterson–Codazzi and Gauss equations in an infinite domain.
Received: 10.12.1974
Citation:
E. V. Shikin, “On the existence of solutions of the system of Peterson–Codazzi and gauss equations”, Mat. Zametki, 17:5 (1975), 765–781; Math. Notes, 17:5 (1975), 455–466
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https://www.mathnet.ru/eng/mzm7597 https://www.mathnet.ru/eng/mzm/v17/i5/p765
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Abstract page: | 341 | Full-text PDF : | 161 | First page: | 1 |
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