Classical differential geometry from the modern viewpoint and its application

本研究从积分系统理论、奇点理论等现代观点出发，对经典微分几何进行了研究，得到了经典微分几何及其应用的各个领域的结果，特别是与可积系统有关的曲线的运动、四维空间型的共形平坦超曲面的显式构造和分类、复杂空间型的实超曲面、三维空间的曲面、仿射微分几何及其在海森几何和信息几何中的应用等。

In this research, we studied classical differential geometry from modern viewpoints, such as of the theory of integral systems and of the theory of singularities ; we obtained results on various fields of classical differential geometry and their applications, in particular, the motions of curves associated with integrable systems, explicit construction and the classification of conformally flat hypersurfaces of four-dimensional space forms, real hypersurfaces of complex space forms, surfaces of three-dimensional spaces, affine differential geometry and its applications to Hessian geometry and information geometry, and so on.