Geodesic
On the existence of solutions of the system of Peterson–Codazzi and gauss equations
Matematičeskie zametki, Tome 17 (1975) no. 5, pp. 765-781 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{MZM_1975_17_5_a10,
     author = {E. V. Shikin},
     title = {On the existence of solutions of the system of {Peterson{\textendash}Codazzi} and gauss equations},
     journal = {Matemati\v{c}eskie zametki},
     pages = {765--781},
     year = {1975},
     volume = {17},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_5_a10/}
}
TY  - JOUR
AU  - E. V. Shikin
TI  - On the existence of solutions of the system of Peterson–Codazzi and gauss equations
JO  - Matematičeskie zametki
PY  - 1975
SP  - 765
EP  - 781
VL  - 17
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MZM_1975_17_5_a10/
LA  - ru
ID  - MZM_1975_17_5_a10
ER  - 
%0 Journal Article
%A E. V. Shikin
%T On the existence of solutions of the system of Peterson–Codazzi and gauss equations
%J Matematičeskie zametki
%D 1975
%P 765-781
%V 17
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_1975_17_5_a10/
%G ru
%F MZM_1975_17_5_a10
E. V. Shikin. On the existence of solutions of the system of Peterson–Codazzi and gauss equations. Matematičeskie zametki, Tome 17 (1975) no. 5, pp. 765-781. http://geodesic.mathdoc.fr/item/MZM_1975_17_5_a10/