## Advanced Studies in Pure Mathematics

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

#### 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

Dates
Revised: 31 March 2015
First available in Project Euclid: 4 October 2018

https://projecteuclid.org/ euclid.aspm/1538671775

Digital Object Identifier
doi:10.2969/aspm/07210349

Mathematical Reviews number (MathSciNet)
MR3726718

Zentralblatt MATH identifier
1386.53096

#### 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