# A few remarks on the geometry of the space of leaf closures of a Riemannian foliation

Małgorzata Józefowicz; R. Wolak

Banach Center Publications (2007)

- Volume: 76, Issue: 1, page 395-409
- ISSN: 0137-6934

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topMałgorzata Józefowicz, and R. Wolak. "A few remarks on the geometry of the space of leaf closures of a Riemannian foliation." Banach Center Publications 76.1 (2007): 395-409. <http://eudml.org/doc/281631>.

@article{MałgorzataJózefowicz2007,

abstract = {The space of the closures of leaves of a Riemannian foliation is a nice topological space, a stratified singular space which can be topologically embedded in $ℝ^k$ for k sufficiently large. In the case of Orbit Like Foliations (OLF) the smooth structure induced by the embedding and the smooth structure defined by basic functions is the same. We study geometric structures adapted to the foliation and present conditions which assure that the given structure descends to the leaf closure space. In Section 5 we introduce the notion of an Ehresmann connection on a stratified foliated space and study the properties of the strata which depend on the existence of such a connection. We also give conditions which ensure that a connection understood as a differential operator defines an Ehresmann connection as above. In the last section we present some curvature estimates for metric structures on the leaf closure space.},

author = {Małgorzata Józefowicz, R. Wolak},

journal = {Banach Center Publications},

keywords = {transversally Kähler foliation; stratified singular space; leaf space},

language = {eng},

number = {1},

pages = {395-409},

title = {A few remarks on the geometry of the space of leaf closures of a Riemannian foliation},

url = {http://eudml.org/doc/281631},

volume = {76},

year = {2007},

}

TY - JOUR

AU - Małgorzata Józefowicz

AU - R. Wolak

TI - A few remarks on the geometry of the space of leaf closures of a Riemannian foliation

JO - Banach Center Publications

PY - 2007

VL - 76

IS - 1

SP - 395

EP - 409

AB - The space of the closures of leaves of a Riemannian foliation is a nice topological space, a stratified singular space which can be topologically embedded in $ℝ^k$ for k sufficiently large. In the case of Orbit Like Foliations (OLF) the smooth structure induced by the embedding and the smooth structure defined by basic functions is the same. We study geometric structures adapted to the foliation and present conditions which assure that the given structure descends to the leaf closure space. In Section 5 we introduce the notion of an Ehresmann connection on a stratified foliated space and study the properties of the strata which depend on the existence of such a connection. We also give conditions which ensure that a connection understood as a differential operator defines an Ehresmann connection as above. In the last section we present some curvature estimates for metric structures on the leaf closure space.

LA - eng

KW - transversally Kähler foliation; stratified singular space; leaf space

UR - http://eudml.org/doc/281631

ER -

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