International Journal of Differential Equations

A Measurable Stability Theorem for Holomorphic Foliations Transverse to Fibrations

Bruno Scardua

Full-text: Open access

Abstract

We prove that a transversely holomorphic foliation, which is transverse to the fibers of a fibration, is a Seifert fibration if the set of compact leaves is not a zero measure subset. Similarly, we prove that a finitely generated subgroup of holomorphic diffeomorphisms of a connected complex manifold is finite provided that the set of periodic orbits is not a zero measure subset.

Article information

Source
Int. J. Differ. Equ., Volume 2012 (2012), Article ID 585298, 6 pages.

Dates
Received: 22 May 2012
Accepted: 22 July 2012
First available in Project Euclid: 24 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1485226822

Digital Object Identifier
doi:10.1155/2012/585298

Mathematical Reviews number (MathSciNet)
MR2959773

Zentralblatt MATH identifier
1248.32015

Citation

Scardua, Bruno. A Measurable Stability Theorem for Holomorphic Foliations Transverse to Fibrations. Int. J. Differ. Equ. 2012 (2012), Article ID 585298, 6 pages. doi:10.1155/2012/585298. https://projecteuclid.org/euclid.ijde/1485226822


Export citation

References

  • C. Camacho and A. Lins Neto, Geometric Theory of Foliations, Birkhäuser, Boston, Mass, USA, 1985.
  • C. Godbillon, “Foliations,” in Geometric Studies, Progress in Mathematics, 98, Birkhäuser, Basel, Switzerland, 1991.
  • B. Scárdua, “On complex codimension-one foliations transverse fibrations,” Journal of Dynamical and Control Systems, vol. 11, no. 4, pp. 575–603, 2005.
  • B. A. Scárdua, “Holomorphic foliations transverse to fibrations on hyperbolic manifolds,” Complex Variables. Theory and Application, vol. 46, no. 3, pp. 219–240, 2001.
  • F. Santos and B. Scardua, “Stability of complex foliations transverse to fibrations,” Proceedings of the American Mathematical Society, vol. 140, no. 9, pp. 3083–3090, 2012.
  • B. Scárdua, “Complex vector fields having orbits with bounded geometry,” The Tohoku Mathematical Journal, vol. 54, no. 3, pp. 367–392, 2002.
  • W. Burnside, “On criteria for the finiteness of the order of a group of linear substitutions,” Proceedings of the London Mathematical Society, vol. 3, no. 2, pp. 435–440.
  • I. Schur, “Über Gruppen čommentComment on ref. [8?]: Please provide complete journal name in this reference, if possible. periodischer substitutionen,” Sitzungsber. Preuss. Akad. Wiss, pp. 619–627, 1911.