Non-diffeomorphic Reeb foliations and modified Godbillon-Vey class

@article{Bazaikin2021NondiffeomorphicRF,
  title={Non-diffeomorphic Reeb foliations and modified Godbillon-Vey class},
  author={Ya.V. Bazaikin and Anton S. Galaev and Pavel Gumenyuk},
  journal={Mathematische Zeitschrift},
  year={2021}
}
The definition of the Reeb foliation depends upon two real functions satisfying certain conditions. All these foliations are pairwise homeomorphic and have trivial Godbillon-Vey class. We construct explicit examples of the Reeb foliations that are not diffeomorphic. For this purpose we show that a modified Godbillon-Vey class defined by Losik is non-trivial for some Reeb foliations and trivial for some other Reeb foliations. This characteristic class takes values in the second order frame… 
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