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Results in Mathematics

, 56:211 | Cite as

Codazzi-Equivalent Affine Connections

  • Angela Schwenk-SchellschmidtEmail author
  • Udo Simon
Article

Abstract.

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].

Mathematics Subject Classification (2000).

53B05 53A15 53B25 53C40 58J05 

Keywords.

Affine connections Codazzi-equivalence conjugate connections relative Gauß maps parallel hypersurfaces 

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Fachbereich Mathematik – Physik – ChemieBHT BerlinBerlinGermany
  2. 2.Institut MathematikTU BerlinBerlinGermany

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