本项目以有限域上正交群的几何空间中所有 m 维全迷向(或全奇异)子空间为点集构作了一类图，称之为有限正交几何图。我们拟通过群论、有限几何、矩阵几何等相关理论知识研究它们的自同构群及其次成分的结构。对这些问题的研究是当前代数图论中的一个重要而饶有兴趣的课题，该问题得以解决不但会使其本身的理论得到不断完善，也将会对相关数学分支之间的相互渗透产生积极影响。

In this project, we construct a class of graphs by all m-dimensional totally isotropic (or singular) subspaces of the geometry of orthogonal group over finite fields, called finite orthogonal geometry graph. We will investigate the automorphism groups of the graphs and their subconsitituents by using the theories of group, finite geometry, geometry of matrices and so on. The investigation of these problems is currently an important and interesting topic in the research areas of algebraic graph theory. The accomplishment of these problems will not only improve the theories of themselves, but also exert a positive impact on the interpenetration among related mathematics branches.