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This analysis defines holomorphic foliations on tori, proving transversely holomorphic Cartan geometries are flat.
We define a class of nonsingular holomorphic foliations on compact complex tori which generalizes (in higher codimension) the turbulent foliations of codimension one constructed by Ghys. For those smooth turbulent foliations we prove that all transversely holomorphic Cartan geometries are flat. We also establish a uniqueness result for the transversely holomorphic Cartan geometries.
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Biswas et al. (2025) studied this question.
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