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.