论文标题
具有HESSIAN等级2的仿射均匀表面和差分代数
Affine Homogeneous Surfaces with Hessian rank 2 and Algebras of Differential Invariants
论文作者
论文摘要
考虑一个$ \ mathbb {c}^3_ {x，y，u} $在仿射转换组$ a（3）$的动作下，请考虑$ \ mathbb {c}^3_ {c}^3_ {c}^3_ {c}^3_ {c}^3_ {c}^3_ {c}^3_ 3_（3）$。 1999年，伊斯特伍德（Eastwood）和埃兹霍夫（Ezhov）通过确定可能的切向量矢量场获得了均匀模型的列表。受奥尔弗（Olver）的复发公式的启发，我们研究了$ a（3）$差异表面的代数。我们获得了代数性质同质性的必要条件。解决这些条件，我们在不相等的分支中组织了同质模型。
Consider a graphed holomorphic surface $u=F(x,y)$ in $\mathbb{C}^3_{x,y,u}$ under the action of the affine transformation group $A(3)$. In 1999, Eastwood and Ezhov obtained a list of homogeneous models by determining possible tangential vector fields. Inspired by Olver's recurrence formulas, we study the algebra of $A(3)$ differential invariants of surfaces. We obtain necessary conditions for homogeneity of algebraic nature. Solving these conditions, we organise homogeneous models in inequivalent branches.
