A Burns-Epstein invariant for ACHE 4-manifolds

On the Burns-Epstein invariants of spherical CR 3-manifolds

In this paper we develop a method to compute the Burns-Epstein invariant of a spherical CR homology sphere, up to an integer, from its holonomy representation. As application, we give a formula for the Burns-Epstein invariant, modulo an integer, of a spherical CR structure on a Seifert fibered homology sphere in terms of its holonomy representation.

CR几何中的二次特征类

Secondary Characteristic Classes in CR Geometry

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。

Sasakian $η$-Einstein流形的若干整体CR不变量公式

Formulae of some global CR invariants for Sasakian $η$-Einstein manifolds

针对Sasakian $η$-Einstein流形，利用丸亀的重整化特征形式给出Burns-Epstein不变量及整体CR不变量的显式公式，并证明后者代数独立。

Flag structures on real 3-manifolds

We define flag structures on a real three manifold M as the choice of two complex lines on the complexified tangent space at each point of M. We suppose that the plane field defined by the complex lines is a contact plane and construct an adapted connection on an appropriate principal bundle. This includes path geometries and CR structures as special cases. We prove that the null curvature models are given by totally real submanifolds in the flag space SL(3, C)/B, where B is the subgroup of upper triangular matrices. We also define a global invariant which is analogous to the Chern-Simons seco…

The $P^\prime$-operator, the $Q^\prime$-curvature, and the CR tractor calculus

We establish an algorithm which computes formulae for the CR GJMS operators, the $P^\prime$-operator, and the $Q^\prime$-curvature in terms of CR tractors. When applied to torsion-free pseudo-Einstein contact forms, this algorithm both gives an explicit factorisation of the CR GJMS operators and the $P^\prime$-operator, and shows that the $Q^\prime$-curvature is constant, with the constant explicitly given in terms of the Webster scalar curvature. We also use our algorithm to derive local formulae for the $P^\prime$-operator and $Q^\prime$-curvature of a five-dimensional pseudo-Einstein manifo…

Embeddability for Three-Dimensional Cauchy-Riemann Manifolds and CR Yamabe Invariants

Let M^3 be a closed CR 3-manifold. In this paper we derive a Bochner formula for the Kohn Laplacian in which the pseudo-hermitian torsion plays no role. By means of this formula we show that the non-zero eigenvalues of the Kohn Laplacian are bounded below by a positive constant provided the CR Paneitz operator is non-negative and the Webster curvature is positive. Our lower bound for the non-zero eigenvalues is sharp and is attained on S^3. A consequence of our lower bound is that all compact CR 3-manifolds with non-negative CR Paneitz operator and positive CR Yamabe constant are embeddable. N…