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Affine conormal of convex hypersurfaces

Author: Chi-Ming Yau
Journal: Proc. Amer. Math. Soc. 106 (1989), 465-470
MSC: Primary 53A15; Secondary 53C40
MathSciNet review: 965947
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Abstract: The geometry of convex hypersurfaces in real affine space is analyzed using the affine conormal. A weak version of Chern's conjecture, characterizing paraboloids among convex graphs, is proved. In addition, it is shown that a closed convex affine hypersurface with constant affine total curvature is an ellipsoid.

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Keywords: Convex affine hypersurface, Chern's conjecture, affine conormal, affine total curvature, ellipsoid
Article copyright: © Copyright 1989 American Mathematical Society

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