Assertion: foliation | /r/HasProperty | structured like fibration
Facets:
value: under certain conditions
type: OTHER
Source sentences:
text: In this much attention was paid to foliations of codimension 1, the existence of compact leaves, stability theorems (establishing that, under certain conditions, foliations with a compact leaf are structured like fibrations, in a neighbourhood of the leaf or globally; the first theorems of this type were already proved by Reeb, see ), the "growth" characteristic of the leaves (that is, the dependence on $ r $ of the $ p $- dimensional volume of a geodesic sphere of radius $ r $ on a leaf), and their fundamental groups.
text: In this much attention was paid to foliations of codimension 1, the existence of compact leaves, stability theorems (establishing that, under certain conditions, foliations with a compact leaf are structured like fibrations, in a neighbourhood of the leaf or globally; the first theorems of this type were already proved by Reeb, see ), the "growth" characteristic of the leaves (that is, the dependence on $ r $ of the $ p $- dimensional volume of a geodesic sphere of radius $ r $ on a leaf), and their fundamental groups.