Geodesic
Compact spacelike surfaces in the 3-dimensional de Sitter space
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 2 (2006) no. 1, pp. 3-8 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We establish several sufficient conditions for a compact spacelike surface in the 3-dimensional de Sitter space to be totally geodesic or spherical. 
@article{JMAG_2006_2_1_a0,
     author = {A. A. Borisenko},
     title = {Compact spacelike surfaces in the 3-dimensional de {Sitter} space},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {3--8},
     year = {2006},
     volume = {2},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2006_2_1_a0/}
}
TY  - JOUR
AU  - A. A. Borisenko
TI  - Compact spacelike surfaces in the 3-dimensional de Sitter space
JO  - Žurnal matematičeskoj fiziki, analiza, geometrii
PY  - 2006
SP  - 3
EP  - 8
VL  - 2
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JMAG_2006_2_1_a0/
LA  - en
ID  - JMAG_2006_2_1_a0
ER  - 
%0 Journal Article
%A A. A. Borisenko
%T Compact spacelike surfaces in the 3-dimensional de Sitter space
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2006
%P 3-8
%V 2
%N 1
%U http://geodesic.mathdoc.fr/item/JMAG_2006_2_1_a0/
%G en
%F JMAG_2006_2_1_a0
A. A. Borisenko. Compact spacelike surfaces in the 3-dimensional de Sitter space. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 2 (2006) no. 1, pp. 3-8. http://geodesic.mathdoc.fr/item/JMAG_2006_2_1_a0/

[1] G. M. Adelson-Vel'sky, “The generalization of one geometrical theorem of S. N. Bernshtein”, Dokl. Akad. Nauk USSR, 49 (1945), 6 (Russian)

[2] J. A. Aledo, A. Romero, “Compact spacelike surfaces in the 3-dimensional de Sitter space with nondegenerate second fundamental form”, Diff. Geom. and its Appl., 19 (2003), 97–111 | DOI | MR | Zbl

[3] A. D. Aleksanrdov, “On the curvature of surfaces”, Vestnik Leningr. Univ. Ser. Mat. Mech. Astrs., 19:4 (1966), 5–11 (Russian) | MR

[4] S. N. Bernshtein, Amplification of the theorem of surfaces with negative curvature, Sobr. Soch., v. 3, Publ. House Akad. Nauk USSR, Moscow, 1960 (Russian)

[5] Russian Math. Surveys, 54:5 (1999), 1021–1022 | DOI | DOI | MR | Zbl

[6] Mat. Sb., 33 (1977), 485–499 | DOI | MR | Zbl | Zbl

[7] Mat. Sb., 42 (1982), 297–310 | DOI | MR | Zbl

[8] H. Li, “Global rigidity theorems of hypersurfaces”, Ark. Mat., 35 (1997), 327–351 | DOI | MR | Zbl

[9] S. Montiel, “An integral inequality for compact spacelike hypersurfaces in de Sitter space and applications to the case of constant mean curvature”, Indiana Univ. Math. J., 37 (1988), 909–917 | DOI | MR | Zbl

[10] J. Ramanathan, “Complete spacelike hypersurfaces of constant mean curvature in de Sitter space”, Indiana Univ. Math. J., 36 (1987), 349–359 | DOI | MR | Zbl

[11] D. D. Sokolov, “The structure of the limit cone of a convex surface in pseudo-Euclidean space”, Usp. Mat. Nauk, 30:1(181) (1975), 261–262 (Russian) | MR | Zbl