Advanced Studies in Pure Mathematics

Godbillon–Vey invariants for maximal isotropic $C^{2}$ foliations

Patrick Foulon and Boris Hasselblatt

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

For a contact manifold $(M^{2m+1}, A)$ and an $m+1$-dimensional $dA$-isotropic $C^{2}$ foliation, we define Godbillon–Vey invariants $\{\mathit{GV}_{i}\}_{i = 0}^{m+1}$ inspired by the Godbillon–Vey invariant of a codimension-one foliation, and we demonstrate the potential of this family as a tool in geometric rigidity theory. One ingredient for the latter is the Mitsumatsu formula for geodesic flows on (Finsler) surfaces.

Article information

Source
Geometry, Dynamics, and Foliations 2013: In honor of Steven Hurder and Takashi Tsuboi on the occasion of their 60th birthdays, T. Asuke, S. Matsumoto and Y. Mitsumatsu, eds. (Tokyo: Mathematical Society of Japan, 2017), 349-365

Dates
Received: 29 January 2014
Revised: 31 March 2015
First available in Project Euclid: 4 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1538671775

Digital Object Identifier
doi:10.2969/aspm/07210349

Mathematical Reviews number (MathSciNet)
MR3726718

Zentralblatt MATH identifier
1386.53096

Subjects
Primary: 57D30
Secondary: 57R30: Foliations; geometric theory 53D10: Contact manifolds, general 37D20: Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)

Keywords
Godbillon–Vey invariants contact flow Anosov flow Mitsumatsu formula rigidity

Citation

Foulon, Patrick; Hasselblatt, Boris. Godbillon–Vey invariants for maximal isotropic $C^{2}$ foliations. Geometry, Dynamics, and Foliations 2013: In honor of Steven Hurder and Takashi Tsuboi on the occasion of their 60th birthdays, 349--365, Mathematical Society of Japan, Tokyo, Japan, 2017. doi:10.2969/aspm/07210349. https://projecteuclid.org/euclid.aspm/1538671775


Export citation