Some Theorems in Affine Differential Geometry<sup>*</sup>
Acta Mathematica Sinica, English Series
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Acta Mathematica Sinica, English Series  1989, Vol. 5 Issue (4): 345-354    DOI: 10.1007/BF02107712
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Some Theorems in Affine Differential Geometry*
Li Anmin
Department of Mathematics, Sichuan University
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Abstract In this paper we prove that an affine hypersphere with scalar curvature zero in a unimodular affine space of dimension n+1 must be contained either in an elliptic paraboloid or in an affine image of the hypersurface x1x2xn+1=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.
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Li Anmin
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Received: 1988-07-04;
Fund: * The Project Supported by National Natural Science Foundation of China
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Li Anmin. Some Theorems in Affine Differential Geometry*[J]. Acta Mathematica Sinica, English Series, 1989, 5(4): 345-354.
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http://www.actamath.com/Jwk_sxxb_en//EN/10.1007/BF02107712      or     http://www.actamath.com/Jwk_sxxb_en//EN/Y1989/V5/I4/345
 
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