Geodesic
On the geometric interpretation of solutions of a~system generalizing the sine-Gordon equation
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 1, pp. 93-139.

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

We propose a geometric interpretation of solutions of the system generalizing the well-known sine-Gordon equation. We prove that to any solution of the Efimov–Poznyak system in a simply-connected domain, a $C^{3}$-smooth singular surface with given first fundamrntal bilinear form corresponds. 
@article{FPM_2005_11_1_a3,
     author = {A. V. Bad'in},
     title = {On the geometric interpretation of solutions of a~system generalizing the {sine-Gordon} equation},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {93--139},
     publisher = {mathdoc},
     volume = {11},
     number = {1},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2005_11_1_a3/}
}
TY  - JOUR
AU  - A. V. Bad'in
TI  - On the geometric interpretation of solutions of a~system generalizing the sine-Gordon equation
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2005
SP  - 93
EP  - 139
VL  - 11
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2005_11_1_a3/
LA  - ru
ID  - FPM_2005_11_1_a3
ER  - 
%0 Journal Article
%A A. V. Bad'in
%T On the geometric interpretation of solutions of a~system generalizing the sine-Gordon equation
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2005
%P 93-139
%V 11
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2005_11_1_a3/
%G ru
%F FPM_2005_11_1_a3
A. V. Bad'in. On the geometric interpretation of solutions of a~system generalizing the sine-Gordon equation. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 1, pp. 93-139. http://geodesic.mathdoc.fr/item/FPM_2005_11_1_a3/

[1] Efimov N. V., Poznyak E. G., “Nekotorye preobrazovaniya osnovnykh uravnenii teorii poverkhnostei”, DAN SSSR, 137:1 (1961), 25–27 | MR

[2] Efimov N. V., Poznyak E. G., “Poverkhnosti s medlenno izmenyayuscheisya otritsatelnoi kriviznoi”, Uspekhi mat. nauk, 21:5 (1966), 3–58 | MR | Zbl

[3] Ilin V. A., Poznyak E. G., Lineinaya algebra, Nauka, M., 1984 | MR

[4] Poznyak E. G., “Geometricheskaya interpretatsiya regulyarnykh reshenii uravneniya $Z_{xy}=\sin Z$”, Differents. uravn., 15:7 (1979), 1332–1336 | MR | Zbl

[5] Postnikov M. M., Lektsii po geometrii. Semestr III. Gladkie mnogoobraziya, Nauka, M., 1987 | MR | Zbl

[6] Postnikov M. M., Lektsii po geometrii. Semestr V. Rimanova geometriya, Faktorial, M., 1998

[7] Rashevskii P. K., Rimanova geometriya i tenzornyi analiz, GITTL, M., 1953

[8] Rozendorn E. R., “Issledovanie osnovnykh uravnenii teorii poverkhnostei v asimptoticheskikh koordinatakh”, Mat. sb., 70:4 (1966), 490–507 | MR | Zbl