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October 5, 2025Open Access

Turbulent holomorphic foliations on compact complex tori and transversely holomorphic Cartan geometry

Key Points

All transversely holomorphic Cartan geometries of smooth turbulent foliations are flat.
This work generalizes turbulent foliations from codimension one to higher codimension on compact complex tori.
A uniqueness result is established for transversely holomorphic Cartan geometries.
The findings reveal significant implications in the study of holomorphic geometries on complex tori.

Abstract

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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Cite This Study

Biswas et al. (Thu,) studied this question.

synapsesocial.com/papers/68e25385d6d66a53c2474e1d https://doi.org/https://doi.org/10.48550/arxiv.2510.01804