仿射微分几何是微分几何学的重要分支之一, 而仿射超曲面是仿射微分几何主要的研究对象。目前，对于仿射超曲面的研究，无论是从整体还是局部都有很多有趣的结果，但也遗留了一些重要的问题未能解决。另一方面，具有典型几何性质的仿射超曲面越来越受到重视，但有效的研究方法较少且相对困难。. 综上所述，本项目拟在已有的工作基础上，对下述三个方面展开研究：（1）局部强凸的等参或齐性仿射超曲面的构造和分类；（2）仿射球Calabi型复合的特征刻画及其应用；（3）具有典型几何性质的仿射超曲面的分类，例如：具常截面曲率和消失Pick不变量的仿射球，具有平行cubic形式或自合同中心映射的非退化仿射超曲面。

Affine differential geometry is one of the most important components in differential geometry, while affine hypersurface is the main subject for the study of affine differential geometry. Now, for the study of affine hypersurface, on both whole and local geometry there are many interesting results, but which also left some important questions. On the other hand, affine hypersurfaces with canonical geometry properties are payed more and more attention, but few methods are allowable and the study is difficult. . In summary, based on our experience of the subject we will study the following three parts: (1) Construction and classification of locally strongly convex isoparametric or homogeneous affine hypersurfaces; (2) Characterization of the Calabi-type composition of affine spheres and its application; (3) Classification of the affine hypersurfaces with canonical geometry properties, for example, the affine spheres have constant sectional curvature and vanishing Pick invariant, and the non-degenerate affine hypersurfaces have parallel cubic form or self-congruent center map.