论文标题
$ \ MATHCAL {i}^\ prime $ -Curvatures在更高维度和Hirachi猜想中
$\mathcal{I}^\prime$-curvatures in higher dimensions and the Hirachi conjecture
论文作者
论文摘要
我们构建了$ \ MATHCAL {i}^\ prime $ - casuvature的更高维度类似物，并在所有Cr尺寸中构建了$ n \ geq2 $。我们的$ \ Mathcal {i}^\ prime $ -curvatures在接触形式的更改下，一阶线性差速器操作员都会通过一阶线性差异操作员转换，其总积分独立于封闭的CR歧管上的伪内斯坦触点形式的选择。我们展示了这些总体积分取决于一般接触形式的选择，从而在所有Cr尺寸中对Hirachi猜想进行反例，从而在所有CR级$ N \ GEQ2 $中产生反例。
We construct higher-dimensional analogues of the $\mathcal{I}^\prime$-curvature of Case and Gover in all CR dimensions $n\geq2$. Our $\mathcal{I}^\prime$-curvatures all transform by a first-order linear differential operator under a change of contact form and their total integrals are independent of the choice of pseudo-Einstein contact form on a closed CR manifold. We exhibit examples where these total integrals depend on the choice of general contact form, and thereby produce counterexamples to the Hirachi conjecture in all CR dimensions $n\geq2$.
