Geodesic
Nonbendability of closed surfaces of genus $p\geqslant1$ and positive extrinsic curvature
Sbornik. Mathematics, Tome 30 (1976) no. 3, pp. 361-372 
V. T. Fomenko; S. B. Klimentov. Nonbendability of closed surfaces of genus $p\geqslant1$ and positive extrinsic curvature. Sbornik. Mathematics, Tome 30 (1976) no. 3, pp. 361-372. http://geodesic.mathdoc.fr/item/SM_1976_30_3_a5/
@article{SM_1976_30_3_a5,
     author = {V. T. Fomenko and S. B. Klimentov},
     title = {Nonbendability of closed surfaces of genus $p\geqslant1$ and positive extrinsic curvature},
     journal = {Sbornik. Mathematics},
     pages = {361--372},
     year = {1976},
     volume = {30},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1976_30_3_a5/}
}
TY  - JOUR
AU  - V. T. Fomenko
AU  - S. B. Klimentov
TI  - Nonbendability of closed surfaces of genus $p\geqslant1$ and positive extrinsic curvature
JO  - Sbornik. Mathematics
PY  - 1976
SP  - 361
EP  - 372
VL  - 30
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_1976_30_3_a5/
LA  - en
ID  - SM_1976_30_3_a5
ER  - 
%0 Journal Article
%A V. T. Fomenko
%A S. B. Klimentov
%T Nonbendability of closed surfaces of genus $p\geqslant1$ and positive extrinsic curvature
%J Sbornik. Mathematics
%D 1976
%P 361-372
%V 30
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1976_30_3_a5/
%G en
%F SM_1976_30_3_a5

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

This paper contains a proof of the unbendability of a closed surface of genus $p>1$ and positive extrinsic curvature in a $3$-dimensional Riemannian space, and the unbendability of a closed surface of genus $p=1$ and positive extrinsic curvature in a Riemannian space when one point of the surface is fixed. Bibliography: 8 titles.

[1] I. N. Vekua, Obobschennye analiticheskie funktsii, Fizmatgiz, Moskva, 1959 | MR

[2] A. V. Pogorelov, Vneshnyaya geometriya vypuklykh poverkhnostei, izd-vo «Nauka», Moskva, 1969 | MR

[3] V. T. Fomenko, “O zhestkosti i odnoznachnoi opredelennosti zamknutykh poverkhnostei roda $p\geqslant1$ v rimanovom prostranstve”, DAN SSSR, 213:1 (1973), 45–48 | MR | Zbl

[4] Yu. L. Rodin, Sistemy differentsialnykh uravnenii 1-go poryadka na zamknutykh rimanovykh poverkhnostyakh, Doktorskaya dissertatsiya, Tbilisi, 1965

[5] S. Ya. Gusman, Yu. L. Rodin, “Yadro integrala tipa Koshi na zamknutykh rimanovykh poverkhnostyakh”, Sib. matem. zh., 3:4 (1962), 527–531 | MR | Zbl

[6] Dzh. Springer, Vvedenie v teoriyu rimanovykh poverkhnostei, IL, Moskva, 1960

[7] S. Sternberg, Lektsii po differentsialnoi geometrii, izd-vo «Mir», Moskva, 1970 | MR

[8] O. A. Ladyzhenskaya, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, izd-vo «Nauka», Moskva, 1973 | MR