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Isometric embeddings in R3 of an annulus with a locally euclidean metric which are multivalued of cylindrical type

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Abstract

It is proved that a locally Euclidean metric on a circular annulus admitting an isometric immersion in R2 which is multivalued of cylindrical type can be isometrically embedded in R3 as a cylindrical surface.

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References

  1. I. N. Vekua, Generalized Analytic Functions (Fizmatlit, Moscow, 1959) [in Russian].

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  2. I. Kh. Sabitov, “Isometric immersions and embeddings of locally Euclidean metrics in R2,” Izv. Ross. Akad. Nauk Ser. Mat. 63 (6), 147–166 (1999) [Izv. Math. 63 (6), 1203–1220 (1999)].

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  3. I. Kh. Sabitov, “Isometric immersion of locally Euclidean metrics in R3,” Sibirsk. Mat. Zh. 26 (3), 156–167 (1985) [Siberian Math. J. 26, 431–440 (1985)].

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  4. S. N. Mikhalev and I. Kh. Sabitov, “Isometric embeddings of locally Euclidean metrics in R3 as conical surfaces,” Mat. Zametki 95 (2), 234–247 (2014) [Math. Notes 95 (2), 214–225 (2014)].

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    S. N. Mikhalev & I. Kh. Sabitov

Authors
  1. S. N. Mikhalev
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  2. I. Kh. Sabitov
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Correspondence to S. N. Mikhalev.

Additional information

Original Russian Text © S. N. Mikhalev, I. Kh. Sabitov, 2015, published in Matematicheskie Zametki, 2015, Vol. 98, No. 3, pp. 378–385.

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Mikhalev, S.N., Sabitov, I.K. Isometric embeddings in R3 of an annulus with a locally euclidean metric which are multivalued of cylindrical type. Math Notes 98, 441–447 (2015). https://doi.org/10.1134/S0001434615090096

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  • DOI: https://doi.org/10.1134/S0001434615090096

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