Differential operators and relations between G-structures

这是一个非详尽的问题清单，将成为申请人在接下来几年研究的一部分。对于其中的一些，如果合作已经开始或即将成为具体的，我就会指出。当然，这并不排除与其他科学家在相应课题上的合作。该项目旨在回答的主要问题是：(1)找到连接两种不同类型g结构的几何结构，类似于Fefferman结构，将CR-连接到保形几何. ...(2)构造Cartan连接的线性版本（在文献中称为牵引连接）作为一些不变微分算子. ...的自然扩展(3)用延拓法刻画一些线性微分算子的解；找到紧凑流形的消失准则. ...(4)考虑奇异空间（主要是在轨道上）. ...上的g结构

Here is a non-exhaustive list of questions that will be part of the applicant's research in the following years. For some of them, where a collaboration has already begun or is close to become concrete, I indicate it. Of course, this does not exclude cooperation with other scientists on the corresponding topics.The main questions that this project is aiming to answer are:(1) Find geometric constructions that connect two different types of G-structures, analoguousto the Fefferman construction, linking CR- to conformal geometry. ...(2) Construct linear versions of the Cartan connection (known in the literature as tractor connections) as natural extensions of some invariant differential operators. ...(3) Characterize solutions of some linear differential operators using the prolongation procedure;find vanishing criteria for compact manifolds. ...(4) Consider G-structures on singular spaces (mainly on orbifolds). ...