Geodesic
On compact submanifolds of nonpositive external curvature in Riemannian spaces
Matematičeskie zametki, Tome 60 (1996) no. 1, pp. 3-10 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper we consider compact multidimensional surfaces of nonpositive external curvature in a Riemannian space. If the curvature of the underlying space is $\ge1$ and the curvature of the surface is $\le1$, then in small codimension the surface is a totally geodesic submanifold that is locally isometric to the sphere. Under stricter restrictions on the curvature of the underlying space, the submanifold is globally isometric to the unit sphere. 
@article{MZM_1996_60_1_a0,
     author = {A. A. Borisenko},
     title = {On compact submanifolds of nonpositive external curvature in {Riemannian} spaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {3--10},
     year = {1996},
     volume = {60},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_60_1_a0/}
}
TY  - JOUR
AU  - A. A. Borisenko
TI  - On compact submanifolds of nonpositive external curvature in Riemannian spaces
JO  - Matematičeskie zametki
PY  - 1996
SP  - 3
EP  - 10
VL  - 60
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MZM_1996_60_1_a0/
LA  - ru
ID  - MZM_1996_60_1_a0
ER  - 
%0 Journal Article
%A A. A. Borisenko
%T On compact submanifolds of nonpositive external curvature in Riemannian spaces
%J Matematičeskie zametki
%D 1996
%P 3-10
%V 60
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_1996_60_1_a0/
%G ru
%F MZM_1996_60_1_a0
A. A. Borisenko. On compact submanifolds of nonpositive external curvature in Riemannian spaces. Matematičeskie zametki, Tome 60 (1996) no. 1, pp. 3-10. http://geodesic.mathdoc.fr/item/MZM_1996_60_1_a0/

[1] Borisenko A. A., “Ob ekstremalnykh svoistvakh kompaktnykh parabolicheskikh poverkhnostei v rimanovom prostranstve”, Matem. sb., 133 (175):1 (1987), 112–126

[2] Borisenko A. A., “O vneshne geometricheskikh svoistvakh parabolicheskikh poverkhnostei i topologicheskikh svoistvakh sedlovykh poverkhnostei v simmetricheskikh prostranstvakh ranga 1”, Matem. sb., 116 (158):3 (1981), 440–457 | MR | Zbl

[3] Eizenkhart L., Rimanova geometriya, IL, M., 1948

[4] Ferus D., “Totally geodesic foliations”, Math. Ann., 88:4 (1970), 313–317 | DOI | MR

[5] Frankel T., “Manifolds with positive curvature”, Pacif. J. Math., 11 (1961), 165–174 | MR | Zbl

[6] Toponogov V. A., “Nekotorye ekstremalnye teoremy rimanovoi geometrii”, Sib. matem. zh., 10:2 (1967), 459–467