论文标题
CR杀死操作员和CR几何形状中的Bernstein-Gelfand-Gelfand构造
The CR Killing operator and Bernstein-Gelfand-Gelfand construction in CR geometry
论文作者
论文摘要
我们在接触歧管上详细阐述了构造的几乎Cr结构（也称为严格的伪有点几乎可以集成的Cr结构）的拖拉机演算，并且作为应用，作为某些情况下，对于某些拖拉机连接，作为某些情况下，表达了第一个BGG不变的差异操作员$ d_0 $。一个有趣的结果是一个事实是，“修改的”伴随拖拉机连接$ \ tilde {\ nabla} $管理抛物面几何形状的无限变形产生了我们称之为CR杀死操作员作为其第一个BGG操作员的东西，实际上，它与正常的（未编码）的邻接tractor connection and It IT不同意。还讨论了CR杀死操作员与ACHE分析（渐近复杂的双曲线爱因斯坦）指标（或更具体地说是CR阻塞张量）之间的关系。
We elaborate the tractor calculus for compatible almost CR structures (also known as strictly pseudoconvex partially integrable almost CR structures) on contact manifolds, and as an application, express the first BGG invariant differential operator $D_0$ explicitly in some cases, i.e., for some tractor connections. An interesting outcome is the fact that the "modified" adjoint tractor connection $\tilde{\nabla}$ governing infinitesimal deformations of parabolic geometries generates what we call the CR Killing operator as its first BGG operator, and actually, it does not agree with the first BGG operator of the normal (unmodified) adjoint tractor connection. The relationship between the CR Killing operator and analysis of ACHE (asymptotically complex hyperbolic Einstein) metrics, or more specifically the CR obstruction tensor, is also discussed.
