Blaschke hypersurfaces with symmetric shape operator |
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| Authors: | Ying Lu |
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| Affiliation: | [1]School of Mathematical Science, Xiamen University, Xiamen 361005, P. R. China [2]Department of Mathematics, K. U. Leuven, 3030 Leuven, Belgium |
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| Abstract: | A Blaschke hypersurface admits (hat nabla S) symmetry if and only if (hat nabla S(X,Y) = hat nabla S(Y,X)). We prove that the shape operator has only one eigenvalue. And such Blaschke surfaces are classified as affine spheres or ruled surfaces. |
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| Keywords: | Affine differential geometry Blaschke hypersurface ruled surface |
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