Geodesic
On a Berger problem
Matematičeskie zametki, Tome 116 (2024) no. 4, pp. 578-583 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An example of two noncongruent isometric analytic compact surfaces is given as a positive answer to M. Berger's question about the existence of such surfaces.
Keywords: isometry, analytic surfaces
Mots-clés : existence. 
@article{MZM_2024_116_4_a6,
     author = {I. Kh. Sabitov},
     title = {On a {Berger} problem},
     journal = {Matemati\v{c}eskie zametki},
     pages = {578--583},
     year = {2024},
     volume = {116},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2024_116_4_a6/}
}
TY  - JOUR
AU  - I. Kh. Sabitov
TI  - On a Berger problem
JO  - Matematičeskie zametki
PY  - 2024
SP  - 578
EP  - 583
VL  - 116
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MZM_2024_116_4_a6/
LA  - ru
ID  - MZM_2024_116_4_a6
ER  - 
%0 Journal Article
%A I. Kh. Sabitov
%T On a Berger problem
%J Matematičeskie zametki
%D 2024
%P 578-583
%V 116
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_2024_116_4_a6/
%G ru
%F MZM_2024_116_4_a6
I. Kh. Sabitov. On a Berger problem. Matematičeskie zametki, Tome 116 (2024) no. 4, pp. 578-583. http://geodesic.mathdoc.fr/item/MZM_2024_116_4_a6/

[1] M. Berger, Geometry Revealed. A Jacob's Ladder to Modern Higher Geometry, Springer, Heidelberg, 2010 | MR

[2] S. E. Kon-Fossen, “Izgibaemost poverkhnostei v tselom”, UMN, 1936, no. 1, 33–76, pereizdano v knige ; С. Э. Кон-Фоссен, Некоторые вопросы дифференциальной геометрии в целом, Физматгиз, М., 1959 | Zbl | MR

[3] A. I. Bobenko, T. Hoffman, A. O. Sageman-Furnas, Compact Bonnet Pairs: Isometric Tori with the Same Curvatures, arXiv: 2110.06335v2

[4] S. E. Kon-Fossen, “Nezhestkie zamknutye poverkhnosti”, Nekotorye voprosy differentsialnoi geometrii v tselom, Fizmatgiz, M., 1959 | MR

[5] E. Rembs, “Zur Verbiegung von Flächen im Grossen”, Math. Z., 56 (1952), 271–279 | MR

[6] D. A. Trotsenko, “O nezhestkikh analiticheskikh poverkhnostyakh vrascheniya”, Sib. matem. zhurn., 21:5 (1980), 100–108 | MR | Zbl

[7] I. Kh. Sabitov, “Zhestkost i neizgibaemost “v malom” i “v tselom” poverkhnostei vrascheniya s uploscheniyami v polyusakh”, Matem. sb., 204:10 (2013), 127–160 | DOI | MR | Zbl

[8] A. D. Milka, “O tochkakh otnositelnoi nezhestkosti vypukloi poverkhnosti vrascheniya”, Ukr. geom. sb., 1965, no. 1, 65–74 | MR