This article is cited in 5 scientific papers (total in 5 papers)
Local and Global Stability of Compact Leaves and Foliations
N. I. Zhukova
Department of Mechanics and Mathematics Nizhny Novgorod State University, Nizhny Novgorod, Russia
The equivalence of the local stability of a compact foliation to the completeness and the quasi analyticity of its pseudogroup is proved. It is also proved that a compact foliation is locally stable if and only if it has the Ehresmann connection and the quasianalytic holonomy pseudogroup. Applications of these criterions are considered. In particular, the local stability of the complete foliations with transverse rigid geometric structures including the Cartan foliations is shown. Without assumption of the existence of an Ehresmann connection, the theorems on the stability of the compact leaves of conformal foliations are proved. Our results agree with the results of other authors.
Key words and phrases:
foliation, compact foliation, Ehresmann connection for a foliation, holonomy pseudogroup, local stability of leaves.
PDF file (245 kB)
MSC: 57R30, 53D22
N. I. Zhukova, “Local and Global Stability of Compact Leaves and Foliations”, Zh. Mat. Fiz. Anal. Geom., 9:3 (2013), 400–420
Citation in format AMSBIB
\paper Local and Global Stability of Compact Leaves and Foliations
\jour Zh. Mat. Fiz. Anal. Geom.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
M. Ciska-Niedziaomska, “On the extremal function of the modulus of a foliation”, Arch. Math., 107:1 (2016), 89–100
H. I. Zhukova, K. I. Sheina, “Kriterii psevdorimanovosti sloeniya s transversalnoi lineinoi svyaznostyu”, Zhurnal SVMO, 18:2 (2016), 30–40
N. I. Zhukova, “Influence of stratification on the groups of conformal transformations of pseudo-Riemannian orbifolds”, Ufa Math. J., 10:2 (2018), 44–57
A. Yu. Dolgonosova, N. I. Zhukova, “Pseudo-Riemannian foliations and their graphs”, Lobachevskii J. Math., 39:1, SI (2018), 54–64
I N. Zhukova, “Automorphism groups of elliptic $G$-structures on orbifolds”, J. Geom. Phys., 132 (2018), 146–154
|Number of views:|