差异张量平行和半平行的仿射超曲面  

Affine Hypersurfaces with Parallel or Semi-Parallel Difference Tensor

作　　者：张廷枋 

机构地区：[1]南平师专数学系,福建南平353000

出　　处：《数学学报（中文版）》2001年第5期791-804,共14页Acta Mathematica Sinica：Chinese Series

摘　　要：本文用活动标架法证明了：若 Ｍｎ（ｎ≥２）是 ｎ＋１维仿射空间 Ａｎ＋１中非退化的仿射超曲面，（１）若■Ｋ＝０（即差异张量平行），则Ｍ是仿射球，且Ｊ＝０和Ｇ是一个Ｅｉｎｓｔｅｉｎ度量，这里Ｊ是Ｍ的 Ｐｉｃｋ不变量，Ｇ是Ｂｌａｓｃｈｋｅ度量；（２）Ｒ·Ｋ＝０（即差异张量半平行）当且仅当Ｓ＝０（Ｍ为虚仿射球），或者Ｋ＝０（Ｍ为非退化的二次超曲面），这里 Ｒ为诱导仿射联络 ■的黎曼曲率算子．With the method of Moving Frames this paper has proved: If Mn (n ≥2) is a nondegenerate affine hypersurface in An+1, (1) Suppose ■K = 0 (The difference tensor K is parallel), then M is an affine hypersphere with J = 0 and G is an Einstein's affine metric, Here J is Pick invariant of M and G is the Blaschke metric. (2) R' K = 0 (The difference tensor K is semi-parallel) if and only if S = 0 (M is an Amproper affine hypersphere), or K = 0 (M is a quadric).

关 键 词：差异张量 平行 半平行 仿射球 仿射空间 仿射超曲面 

分 类 号：O186.13[理学—数学]