# Connexions affines et projectives sur les surfaces complexes compactes

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We prove that holomorphic normal projective connections on compact complex surfaces are flat. We show that a holomorphic torsion-free affine connection \$ abla\$ on a compact complex surface is locally modelled on a translations-invariant affine connection on \$\C^2\$, except if \$ abla\$ is a generic connection on a principal elliptic bundle over a Riemann surface of genus \$g \geq 2\$, with odd first Betti number. In the last case, the local Killing Lie algebra is of dimension one, generated by the fundamental vector field of the principal fibration.

Autor: Sorin Dumitrescu

Fuente: https://archive.org/