In this paper we prove that an affine hypersphere with scalar curvature zero in a unimodular affine space of dimensionn+1 must be contained either in an elliptic paraboloid or in an affine image of the hypersurfacex &...In this paper we prove that an affine hypersphere with scalar curvature zero in a unimodular affine space of dimensionn+1 must be contained either in an elliptic paraboloid or in an affine image of the hypersurfacex <sub class='a-plus-plus'>1</sub> x <sub class='a-plus-plus'>2</sub>...x <sub class='a-plus-plus'>n+1</sub>=const. We prove also that an affine complete, affine maximal surface is an elliptic paraboloid if its affine normals omit 4 or more directions in general position.展开更多
A Blaschke hypersurface admits S symmetry if and only if S（X, Y） = 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.
基金The Project Supported by National Natural Science Foundation of China
文摘In this paper we prove that an affine hypersphere with scalar curvature zero in a unimodular affine space of dimensionn+1 must be contained either in an elliptic paraboloid or in an affine image of the hypersurfacex <sub class='a-plus-plus'>1</sub> x <sub class='a-plus-plus'>2</sub>...x <sub class='a-plus-plus'>n+1</sub>=const. We prove also that an affine complete, affine maximal surface is an elliptic paraboloid if its affine normals omit 4 or more directions in general position.
文摘A Blaschke hypersurface admits S symmetry if and only if S（X, Y） = 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.
