Isometric Embeddings in~$\mathbb{R}^3$ of an Annulus with a Locally Euclidean Metric which Are Multivalued of Cylindrical Type

S. N. Mikhalev; I. Kh. Sabitov

Geodesic

Parcourir par

Isometric Embeddings in~$\mathbb{R}^3$ of an Annulus with a Locally Euclidean Metric which Are Multivalued of Cylindrical Type

S. N. Mikhalev ; I. Kh. Sabitov

Matematičeskie zametki, Tome 98 (2015) no. 3, pp. 378-385

Voir la notice de l'article provenant de la source Math-Net.Ru

Résumé

It is proved that a locally Euclidean metric on a circular annulus admitting an isometric immersion in $\mathbb R^2$ which is multivalued of cylindrical type can be isometrically embedded in $\mathbb R^3$ as a cylindrical surface.

Keywords: locally Euclidean metric, isometric embedding, isometric immersion, cylindrical surface, planar graph.

@article{MZM_2015_98_3_a5,
     author = {S. N. Mikhalev and I. Kh. Sabitov},
     title = {Isometric {Embeddings} in~$\mathbb{R}^3$ of an {Annulus} with a {Locally} {Euclidean} {Metric} which {Are} {Multivalued} of {Cylindrical} {Type}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {378--385},
     publisher = {mathdoc},
     volume = {98},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2015_98_3_a5/}
}

TY  - JOUR
AU  - S. N. Mikhalev
AU  - I. Kh. Sabitov
TI  - Isometric Embeddings in~$\mathbb{R}^3$ of an Annulus with a Locally Euclidean Metric which Are Multivalued of Cylindrical Type
JO  - Matematičeskie zametki
PY  - 2015
SP  - 378
EP  - 385
VL  - 98
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2015_98_3_a5/
LA  - ru
ID  - MZM_2015_98_3_a5
ER  -

%0 Journal Article
%A S. N. Mikhalev
%A I. Kh. Sabitov
%T Isometric Embeddings in~$\mathbb{R}^3$ of an Annulus with a Locally Euclidean Metric which Are Multivalued of Cylindrical Type
%J Matematičeskie zametki
%D 2015
%P 378-385
%V 98
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2015_98_3_a5/
%G ru
%F MZM_2015_98_3_a5

S. N. Mikhalev; I. Kh. Sabitov. Isometric Embeddings in~$\mathbb{R}^3$ of an Annulus with a Locally Euclidean Metric which Are Multivalued of Cylindrical Type. Matematičeskie zametki, Tome 98 (2015) no. 3, pp. 378-385. http://geodesic.mathdoc.fr/item/MZM_2015_98_3_a5/