Geodesic
Topology of codimension-one foliations of nonnegative curvature
Sbornik. Mathematics, Tome 204 (2013) no. 5, pp. 621-640

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

We show that a transversely oriented $C^2$-foliation of codimension one with nonnegative Ricci curvature on a closed orientable manifold is a foliation with almost no holonomy. This allows us to decompose the manifold into blocks on which this foliation has a simple structure. We also show that a manifold homeomorphic to a 5-dimensional sphere does not admit a codimension-one $C^2$-foliation with nonnegative sectional curvature. Bibliography: 29 titles.
Keywords: Riemannian manifold, curvature.
Mots-clés : foliation 
@article{SM_2013_204_5_a0,
     author = {D. V. Bolotov},
     title = {Topology of codimension-one foliations of nonnegative curvature},
     journal = {Sbornik. Mathematics},
     pages = {621--640},
     publisher = {mathdoc},
     volume = {204},
     number = {5},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2013_204_5_a0/}
}
TY  - JOUR
AU  - D. V. Bolotov
TI  - Topology of codimension-one foliations of nonnegative curvature
JO  - Sbornik. Mathematics
PY  - 2013
SP  - 621
EP  - 640
VL  - 204
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2013_204_5_a0/
LA  - en
ID  - SM_2013_204_5_a0
ER  - 
%0 Journal Article
%A D. V. Bolotov
%T Topology of codimension-one foliations of nonnegative curvature
%J Sbornik. Mathematics
%D 2013
%P 621-640
%V 204
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2013_204_5_a0/
%G en
%F SM_2013_204_5_a0
D. V. Bolotov. Topology of codimension-one foliations of nonnegative curvature. Sbornik. Mathematics, Tome 204 (2013) no. 5, pp. 621-640. http://geodesic.mathdoc.fr/item/SM_2013_204_5_a0/