Geodesic
Quasi-conformal mappings of a surface generated by its isometric transformation, and bendings of the surface onto itself
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 1, pp. 281-288
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is proved that any surface $S^{*}$ isometric to a given compact surface $S$ and disposed sufficiently close to $S$ generates a quasi-conformal mapping of $S$ onto itself. On the base of this result it is proved that a compact surface admitting sliding bendings onto itself is topologically a sphere or a torus and its intrinsic metric is of rotation type. 
@article{FPM_1995_1_1_a15,
     author = {I. Kh. Sabitov},
     title = {Quasi-conformal mappings of a surface generated by its isometric transformation, and bendings of the surface onto itself},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {281--288},
     year = {1995},
     volume = {1},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1995_1_1_a15/}
}
TY  - JOUR
AU  - I. Kh. Sabitov
TI  - Quasi-conformal mappings of a surface generated by its isometric transformation, and bendings of the surface onto itself
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 1995
SP  - 281
EP  - 288
VL  - 1
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/FPM_1995_1_1_a15/
LA  - ru
ID  - FPM_1995_1_1_a15
ER  - 
%0 Journal Article
%A I. Kh. Sabitov
%T Quasi-conformal mappings of a surface generated by its isometric transformation, and bendings of the surface onto itself
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 1995
%P 281-288
%V 1
%N 1
%U http://geodesic.mathdoc.fr/item/FPM_1995_1_1_a15/
%G ru
%F FPM_1995_1_1_a15
I. Kh. Sabitov. Quasi-conformal mappings of a surface generated by its isometric transformation, and bendings of the surface onto itself. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 1, pp. 281-288. http://geodesic.mathdoc.fr/item/FPM_1995_1_1_a15/

[1] I. N. Vekua, Obobschennye analiticheskie funktsii, M., 1959, 628 pp. | MR | Zbl

[2] M. Spivak, A comprehensive introduction to Differential Geometry, 5, Publish or Perish, Berkeley, 1979 | MR | Zbl

[3] E. Rembs, “Infinitesimal Verbiegungen von Flächen in sich”, Math. Nachr., 16 (1957), 134–136 | DOI | MR | Zbl