Geometry of statistical structures and the submanifold theory

统计流形几何与信息几何、仿射微分几何、海森几何等诸多研究领域有着密切的联系。在这个项目中，我们研究了统计流形的子流形理论方面，特别是，我们研究了常数Hessian截面曲率的Hessian流形的构造和分类问题，以及此类空间之间的统计超曲面。此外，通过对复空间形式中黎曼子流形的研究，为建立统计流形的复几何做了准备。

Geometry of statistical manifolds are deeply related to various research fields, for example, information geometry, affine differential geometry, and Hessian geometry. In this project, we researched the submanifold theoretical aspects of statistical manifolds, in particular, we studied construction and classification problems for Hessian manifolds of constant Hessian sectional curvature, and for statistical hypersurfaces between such spaces. Furthermore, through the study of Riemannian submanifolds in complex space forms, we prepared to build complex geometry for statistical manifolds.