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arXiv · 2101.02172

Affine connections on complex compact surfaces and Riccati distributions

Ruben Lizarbe
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Abstract

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

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Ruben Lizarbe. 2021-01-06. Affine connections on complex compact surfaces and Riccati distributions. https://doi.org/10.1007/s00229-022-01435-6

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