• Corpus ID: 118173705

Quasi-umbilical affine hypersurfaces congruent to their centre map

@article{Vanderwinden2012QuasiumbilicalAH,
  title={Quasi-umbilical affine hypersurfaces congruent to their centre map},
  author={A. J. Vanderwinden},
  journal={arXiv: Differential Geometry},
  year={2012}
}
  • A. Vanderwinden
  • Published 1 June 2012
  • Mathematics
  • arXiv: Differential Geometry
In this paper, we study strictly convex affine hypersurfaces centroaffinely congruent to their centre map, in the case when the shape operator has two distinct eigenvalues: one of multiplicity 1, and one nonzero of multiplicity n-1. We show how to construct them from (n-1)-dimensional affine hyperspheres. 
On hypersurfaces satisfying conditions determined by the Opozda–Verstraelen affine curvature tensor
Using the Blaschke-Berwald metric and the affine shape operator of a hypersurface M in the (n+1)-dimensional real affine space we can define some generalized curvature tensor named the

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