Feuilletages conformes

Tarquini, Cédric

doi:10.5802/aif.2025

Cited by 19 publications

(11 citation statements)

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“…In [1,Theorem 4], it is proved that any non-Riemannian conformal foliation of codimension q > 2 on a compact manifold is a transversally homogeneous foliation, which strengthens the results of [2,3].…”

Section: Introductionmentioning

confidence: 58%

Transverse Equivalence of Complete Conformal Foliations

Zhukova

2015

J Math Sci

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We study the problem of classification of complete non-Riemannian conformal foliations of codimension q > 2 with respect to transverse equivalence. It is proved that two such foliations are transversally equivalent if and only if their global holonomy groups are conjugate in the group of conformal transformations of the q-dimensional sphere Conf (S q ). Moreover, any countable essential subgroup of the group Conf (S q ) is realized as the global holonomy group of some non-Riemannian conformal foliation of codimension q. Bibliography: 16 titles.

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Section: Introductionmentioning

confidence: 58%

Transverse Equivalence of Complete Conformal Foliations

Zhukova

2015

J Math Sci

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“…R. Sacksteder [1965] gave a result that can be interpreted as giving a characterization of Riemannian pseudogroups of one-dimensional manifolds. More recently, C. Tarquini [2004] proved that equicontinuous transversely conformal foliations are Riemannian; in the case of dense leaves, this result follows easily from our main theorem.…”

Section: Introductionmentioning

confidence: 59%

Topological description of Riemannian foliations with dense leaves

López¹,

Candel²

2010

Pacific J. Math.

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A foliation is called Riemannian if its holonomy pseudogroup consists of local isometries for some Riemannian metric. By combining the work on Hilbert's fifth problem for local groups with our work on equicontinuous foliated spaces, we prove that, if a foliated space is strongly equicontinuous, locally connected and of finite dimension, has a dense leaf, and has holonomy pseudogroup whose closure is quasianalytic, then it is a Riemannian foliation.MSC2000: 22E05, 57R30, 57S05, 58H99.

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“…Proposition 2.1 ([4, Proposition 8.9, and Theorems 11.1 and 12.1], [45] and [5, Theorems 3.3 and 5.2]). Suppose that H is compactly generated, equicontinuous and strongly quasi-analytic.…”

Section: 1mentioning

confidence: 99%