This paper presents a complete method to prove geometric theorem by decomposing the corresponding polynomial system. into strong regular sets, by which one can compute some components for which the geometry theorem is...This paper presents a complete method to prove geometric theorem by decomposing the corresponding polynomial system. into strong regular sets, by which one can compute some components for which the geometry theorem is true and exclude other components for which the geometry theorem is false. Two examples are given to show that the geometry theorems are conditionally true for some components which are excluded by other methods.展开更多
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
文摘This paper presents a complete method to prove geometric theorem by decomposing the corresponding polynomial system. into strong regular sets, by which one can compute some components for which the geometry theorem is true and exclude other components for which the geometry theorem is false. Two examples are given to show that the geometry theorems are conditionally true for some components which are excluded by other methods.
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.
