子流形几何是黎曼几何的重要组成部分，且与李群、变分学、拓扑、偏微分方程等学科联系密切。其中对称空间中极小球面的刚性和分类问题是子流形几何里的重要研究领域一直备受几何学者重视。从上世纪三十年代开始，实空间形式、复空间形式和复二次超曲面等典型黎曼流形中极小2维球面的几何研究发展迅速。随着研究的深入，对称空间中高维球面子流形的几何研究也越来越受到国内外专家的关注，特别是单位球面和复射影空间中极小3维球面的刚性和分类研究取得诸多重要结果。然而，对于几何结构更复杂的复二次超曲面，几何学者不仅对它的极小3维球面的例子所知甚少，而且关于它的极小3维球面的刚性和分类研究还未系统展开。鉴于此，本项目主要研究复二次超曲面中等变极小3维球面的分类问题，特别专注于n维复二次超曲面中等变CR极小常曲率3维球面和等变全实极小常曲率3维球面的分类研究以及复二次超曲面中极小3维球面的例子构造。

Submanifold geometry is an important part of Riemann geometry, and is closely related to Lie Group, Calculus of Variations, Topology, Partial Differential Equations and other disciplines. The rigidity and classification of minimal spheres of symmetric Spaces are important research fields in the submanifold geometry, which have been paid attention to by geometry scholars. Since the 1930s,the investigations of minimal 2-dimensional spheres in the typical Riemannian manifolds has developed rapidly, such as real space forms, complex space forms and complex hyperquadric. With the development of the research, the geometry of higher-dimensional spherical manifolds in symmetric space has attracted more and more attention from experts at home and abroad. Especially, the research on the rigidity and classification of minimal 3-dimensional spheres in the unit sphere and complex projective space has obtained many important results. However, for the complex hyperquadric with more complex geometric structure, not only the example of its minimal 3-dimensional sphere is not known, but also the research on the rigidity and classification of its minimal 3-dimensional sphere has not been systematically researched. In view of this, this project mainly studies the classification of equivariant minimal 3-dimensional spheres of complex hyperquadric. We will consider the classification of equivariant CR minimal 3-dimensional spheres and equivariant totally real minimal 3-dimensional spheres with constant curvature of n-dimensional complex hyperquadric. We also consider the construction of examples of minimal 3-dimensional spheres of complex hyperquadric.