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.
2010-01-08
教育部博士点基金（20060610004）
国家自然科学基金（10631050）
国家自然科学基金（10771146）
国家973项目（2006CB805905）
Sichuan University，Chengdu， China,
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