CR几何中的二次特征类
Secondary Characteristic Classes in CR Geometry
AI总结：
该研究为特定CR流形构造$\boldsymbol{\rm R/Z}$值CR不变量，推导体-边界公式并得到CR嵌入复欧氏空间的阻碍，推广了相关经典结果。
AI中文摘要：
我们为允许伪爱因斯坦接触形式的紧致严格伪凸CR流形构造了一族取值于$\boldsymbol{\rm R/Z}$的CR不变量。通过将Cheeger–Simons微分特征理论应用于法 tractor 联络的全局定义修正来定义这些不变量。当CR全纯切丛平凡时，其自然的$\boldsymbol{\rm R}$值提升与广义Burns–Epstein不变量一致。对于作为相对紧致严格伪凸域边界的CR流形，我们将这些微分特征与重正化联络确定的微分特征等同，并推导了包含重正化特征数和陈类留数的体-边界公式，这些公式恢复并推广了Burns–Epstein和Marugame的结果，我们还得到了CR流形复欧氏空间嵌入的阻碍。
英文摘要：
We construct a family of $\mathbb{R}/\mathbb{Z}$-valued CR invariants for compact strictly pseudoconvex CR manifolds admitting pseudo-Einstein contact forms. We define these invariants by applying the theory of Cheeger--Simons differential characters to a globally defined modification of the normal tractor connection. When the CR holomorphic tangent bundle is trivial, their natural $\mathbb{R}$-valued lifts agree with the generalized Burns--Epstein invariants. For CR manifolds arising as boundaries of relatively compact strictly pseudoconvex domains, we identify these differential characters with those determined by the renormalized connection and derive bulk--boundary formulas involving renormalized characteristic numbers and residues of Chern classes. These formulas recover and extend the results of Burns--Epstein and Marugame. We also obtain obstructions to CR embeddings into complex Euclidean space.
