Connexions affines et projectives sur les surfaces complexes compactesReport as inadecuate



 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.



Author: Sorin Dumitrescu

Source: https://archive.org/







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