Differential operators and relations between G-structures

以下是申请者在未来几年将进行研究的问题的非详尽清单。对于其中一些已经开始或即将成为具体合作的国家，我指出。当然，这并不排除与其他科学家在相应主题上的合作。本项目旨在回答的主要问题是：(1)寻找连接两种不同类型G-结构的几何结构，类似于Fefferman结构，将CR-连接到共形几何。(2)构造Cartan联络(文献中称为拖拉机联络)的线性形式，作为某些不变微分算子的自然扩张.利用延拓方法刻画了一类线性微分算子的解，得到了紧致流形的零化判据.(4)考虑奇异空间上的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). ...