Codazzi-Equivalent Affine Connections
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We extend the concept of Codazzi-equivalence from Riemannian metrics in  to affine connections. Applications to relative hypersurface theory show that this concept simplifies the investigation of pairs of hypersurfaces with parallel normalization, moreover we get a better understanding of the affine Gauß maps. We give a new proof of Calabi’s global affine Minkowski problem; see [1, 10].