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Let $M$ be a complex surface. We show that there is a one-to-onecorrespondence between torsion-free affine connections on $M$ and Riccatidistributions on $\mathbb{P}(TM)$. Furthermore, if $M$ is compact, then thiscorrespondence induces a one-to-one correspondence between affine structures on$M$ and Riccati foliations on $\mathbb{P}(TM)$.

Affine connections on complex compact surfaces and Riccati distributions