Interaction of submanifold theory, integrable systems and variational method with a focus on affine differential geometry

我们研究了具有非半简单Tchebychev算子的平面中仿射曲面，证明了如果Pick不变量是常数，那么它就是一个由Meijer g函数描述的中仿射极小曲面。我们还将以原点为中心的适当仿射球的自然推广——中仿射极小曲面视为射影空间中的曲面，并对相关曲面为射影极小面的曲面进行了分类。我们还研究了用复化正交网参数化的复化球面上的曲面。此外，我们引入了闭等熵仿射平面曲线空间上的可数无限个前辛结构，并证明了这种空间可以用多哈密顿系统来描述。

We studied flat centroaffine surfaces with non-semisimple Tchebychev operator and showed that if the Pick invariant is constant then it is a centroaffine minimal surfaces described by the Meijer G-function. We also regarded centroaffine minimal surfaces, which is a natural generalization of proper affine spheres centered at the origin, as surfaces in the projective space and classified such surfaces whose associated surfaces are projective minimal.We also studied surfaces in the complexified sphere parametrized by a complexified orthogonal net. Moreover, we introduced the countably infinite number of presymplectic structures on the space of closed equicentroaffine plane curves and showed that such a space can be described by multi-hamiltoninan system.