We prove that any holomorphic geometric structure of algebraic type on an Oeljeklaus- Toma manifold is locally homogeneous. For locally conformal K\"ahler Oeljeklaus-Toma manifolds we prove that all holomorphic geometric structures, and also all holomorphic Cartan geometries, on them are locally homogeneous.
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Biswas et al. (2024) studied this question.
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