Summary
A surface in ℝ4 is called affine umbilical if for each vector belonging to the affine normal plane the corresponding shape operator is a multiple of the identity. We will classify affine umbilical definite surfaces which either have constant curvature or which satisfy ∇⊥ g ⊥. Furthermore, it will be shown that for an affine umbilical definite surface, the affine mean curvature vector can not have constant non-zero length.
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The last author is a Senior Research Assistant of the National Fund for Scientific Research (Belgium)
This article was processed by the author using the Springer-Verlag TEX PJour1g macro package 1991.
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Magid, M., Scharlach, C. & Vrancken, L. Affine umbilical surfaces inR 4 . Manuscripta Math 88, 275–289 (1995). https://doi.org/10.1007/BF02567823
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DOI: https://doi.org/10.1007/BF02567823