Applying the method of Moving Frames,we prove a famous Theorem due to N.Boken,K.Nomizu and U.Simon in :If M n(n≥2) is a nondegenerate affine hypersurface in A n+1 ,then both C and 2C are totally ...Applying the method of Moving Frames,we prove a famous Theorem due to N.Boken,K.Nomizu and U.Simon in :If M n(n≥2) is a nondegenerate affine hypersurface in A n+1 ,then both C and 2C are totally symmertric if and only if C=0 (M is a quadric) or S=0 (M is an improper affine hypersphere). Moreover,we improve the conditions of Theorem 2 and its Corollary in .also prove, if ^ C=0 and the affine metric G is of constant curvature α, then M is an affine hypersphere and a=0 or C=0.展开更多
文摘Applying the method of Moving Frames,we prove a famous Theorem due to N.Boken,K.Nomizu and U.Simon in :If M n(n≥2) is a nondegenerate affine hypersurface in A n+1 ,then both C and 2C are totally symmertric if and only if C=0 (M is a quadric) or S=0 (M is an improper affine hypersphere). Moreover,we improve the conditions of Theorem 2 and its Corollary in .also prove, if ^ C=0 and the affine metric G is of constant curvature α, then M is an affine hypersphere and a=0 or C=0.
