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Regular version of the site

Article

Local and global stability of compact leaves and foliations

Journal of Mathematical Physics, Analysis, Geometry. 2013. Vol. 9. No. 3. P. 400-420.

The equivalence between local stability and completeness and Quasi-analyticity is proved for an arbitrary compact foliation. We prove that a compact foliation Locally stable if and only if it admits an Ehresmann connection and has a quasi-analytical holonomy pseudo-group. As an application we prove the local stability of complete compact foliations with a rigid transverse geometry, which included Cartan foliations. Without assumption about the existence of an Ehresmsnn conection we prove two theorems on stability of compact leaves of conformal foliations. The relation with results of other authors is established.