Geodesic
Isometric transformations of a surface inducing conformal maps of the surface onto itself
Sbornik. Mathematics, Tome 189 (1998) no. 1, pp. 115-127 
I. Kh. Sabitov. Isometric transformations of a surface inducing conformal maps of the surface onto itself. Sbornik. Mathematics, Tome 189 (1998) no. 1, pp. 115-127. http://geodesic.mathdoc.fr/item/SM_1998_189_1_a5/
@article{SM_1998_189_1_a5,
     author = {I. Kh. Sabitov},
     title = {Isometric transformations of a~surface inducing conformal maps of the~surface onto itself},
     journal = {Sbornik. Mathematics},
     pages = {115--127},
     year = {1998},
     volume = {189},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1998_189_1_a5/}
}
TY  - JOUR
AU  - I. Kh. Sabitov
TI  - Isometric transformations of a surface inducing conformal maps of the surface onto itself
JO  - Sbornik. Mathematics
PY  - 1998
SP  - 115
EP  - 127
VL  - 189
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1998_189_1_a5/
LA  - en
ID  - SM_1998_189_1_a5
ER  - 
%0 Journal Article
%A I. Kh. Sabitov
%T Isometric transformations of a surface inducing conformal maps of the surface onto itself
%J Sbornik. Mathematics
%D 1998
%P 115-127
%V 189
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1998_189_1_a5/
%G en
%F SM_1998_189_1_a5

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

We consider isometries of a surface inducing, via a specific scheme, conformal maps of the surface onto itself. We give a complete description of the surfaces that admit isometries corresponding to identity conformal maps. For the general case we provide several results and state some unsolved problems.

[1] Sabitov I. Kh., “Kvazikonformnye otobrazheniya poverkhnosti, porozhdennye ee izometricheskimi preobrazovaniyami, i izgibaniya poverkhnosti na sebya”, Fundament. i prikl. matem., 1:1 (1995), 281–288 | MR | Zbl

[2] Sabitov I. Kh., “K voprosu o gladkosti izometrii”, Sib. matem. zhurn., 34:4 (1993), 169–176 | MR | Zbl

[3] Hartman Ph., Wintner A., “On the asymptotic curves of a surface”, Amer. J. Math., 73:1 (1951), 149–172 | DOI | MR | Zbl

[4] Khartman F., Obyknovennye differentsialnye uravneniya, Mir, M., 1970 | MR | Zbl

[5] Ushakov V., Parametrization of developable surfaces by asymptotic lines, Research Report No 43, University of Melburn, 1994, p. 1–9 | Zbl

[6] Hartman Ph., Nirenberg L., “On spherical image maps whose Jacobians do not change sign”, Amer. J. Math., 81:5 (1959), 901–920 | DOI | MR | Zbl

[7] Nevanlinna R., Uniformizatsiya, IL, M., 1955

[8] Spivak M., A comprehensive introduction to Differential Geometry, V. 5, Publish or Perish, Berkley, 1979