Projective Blaschke manifolds
首发时间:2010-01-08
Abstract:In this paper we define the concept of Projective Blaschke manifolds and extend the theory of equiaffine differential geometry to the projective Blaschke manifolds. We prved that if M be a complete projective Blaschke n-sphere and its universal covering manifold is isometric to a complete (n+1) dimensional parabolic, elliptic or hyperbolic affine hypersphere, then M is a quotient space of E^n, S^n or D^n by a isometric subgroup of its corresponding spaces.
keywords: locally projectively flat manifolds equiaffine differential geometry projective Blaschke manifold
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射影Blaschke流形
摘要:在这篇文章中我们定义了射影Blaschke流形的概念,将等仿射微分几何的理论推广到了射影Blaschke流形,并证明:如果n维完备射影Blaschke 超球面 M 的通用覆盖流形分别是完备的抛物型、椭圆型或双曲型仿射球,则M分别是n维欧氏空间、n维超球面 或n维单位圆盘关于各自空间的一个等距离散子群的商,从而对完备射影Blaschke 超球面进行了分类。
关键词: 局部射影平坦流形 等仿射微分几何 射影Blaschke流形
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No.3866351008912629****
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