论文标题
在两个自变量中，pdes的三阶仿射不变（系统）消失了。
Third-order affine-invariant (systems of) PDEs in two independent variables as vanishing of the Fubini-Pick invariant
论文作者
论文摘要
在本文中，我们研究了两个独立变量$ x，y $和一个不变的函数$ u $在$ 3^{\ mathrm {rd}} $ order（of System of PDES的系统中），与仿射转换$ \ mathrm {aff}（aff}（3）$ $ \ \ m i \ mathbbbb {r} r} r} $ \ mathrm {aff}（aff}（3）$）相对于一组不变的函数$ u $。在证明了它们与fubini-pick不变的关系之后，我们使用[d.v. d.v. Alekseevsky，J。Gutt，G。Manno和G. Moreno：在同质流形上构建不变的{pdes}的一般方法。当代数学的通信（2021）]，阐明了它们的一些几何特性。
In this paper we study $3^{\mathrm{rd}}$ order (system of) PDEs in two independent variables $x,y$ and one unknown function $u$ that are invariant with respect to the group of affine transformation $\mathrm{Aff}(3)$ of $\mathbb{R}^3=\{(x,y,u)\}$. After proving their relationship with the Fubini-Pick invariant, we derive the aforementioned PDEs by using a general method introduced in [D.V. Alekseevsky, J. Gutt, G. Manno, and G. Moreno: A general method to construct invariant {PDEs} on homogeneous manifolds. Communications in Contemporary Mathematics (2021)], which sheds light on some of their geometrical properties.
