论文标题
正式自动化联合协方差的多差异操作员的一些构造
Some constructions of formally self-adjoint conformally covariant polydifferential operators
论文作者
论文摘要
我们介绍了正式自我伴侣共同协变的多差异操作员的概念，并给出了此类运营商家庭的一些构造。在一个方向上，我们表明任何同质性变异标量riemannian不变性（CVI）都会诱导其中一个操作员之一。在另一个方向上，我们使用环境指标为以这种方式生产的某些操作员提供了替代构造，其中之一是一种正式的自动化，四阶，共同协变的triDifferential operator，应该被视为Paneitz Operator的最简单的完全非线性类似物。
We introduce the notion of formally self-adjoint conformally covariant polydifferential operators and give some constructions of families of such operators. In one direction, we show that any homogeneous conformally variational scalar Riemannian invariant (CVI) induces one of these operators. In another direction, we use the ambient metric to give alternative constructions of certain operators produced this way, one of which is a formally self-adjoint, fourth-order, conformally covariant tridifferential operator which should be regarded as the simplest fully nonlinear analogue of the Paneitz operator.
