Codazzi-Equivalent Affine Connections

. We extend the concept of Codazzi-equivalence from Riemannian metrics in [14] 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...

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Bibliographic Details
Published in:Resultate der Mathematik 2009-12, Vol.56 (1-4), p.211-229
Main Authors: Schwenk-Schellschmidt, Angela, Simon, Udo
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:. We extend the concept of Codazzi-equivalence from Riemannian metrics in [14] 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].
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-009-0420-y