Geodesic Rigidity of Conformal Connections on Surfaces

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  1. As usual, by an affine torsion-free connection on \(\Sigma\) we mean a torsion-free connection on \(T\Sigma\).

  2. We define \(\varepsilon_{ij}=-\varepsilon_{ji}\) with \(\varepsilon_{12}=1\).

  3. In order to keep notation uncluttered we omit writing \(\lambda^*\) for pull-backs by \(\lambda\).