论文标题
均匀二阶哈密顿运营商的射影几何形状
Projective geometry of homogeneous second order Hamiltonian operators
论文作者
论文摘要
我们证明了在投射互惠转换的作用下，证明了同质二阶汉密尔顿运营商的不变性。我们在尺寸$ n $和$ 3 $ dimension $ n + 1 $的尺寸和3 $ forms中建立了对应关系。通过这种方式，我们使用已知的$ 3 $形式的二级分类对二阶汉密尔顿运营商进行分类，$ \ leq $9。也明确发现了对此类运营商的一阶保护法的系统。详细讨论了系统的集成性。
We prove the invariance of homogeneous second-order Hamiltonian operators under the action of projective reciprocal transformations. We establish a correspondence between such operators in dimension $n$ and $3$-forms in dimension $n + 1$. In this way we classify second order Hamiltonian operators using the known classification of $3$-forms in dimensions $\leq$ 9. Systems of first-order conservation laws that are Hamiltonian with respect to such operators are also explicitly found. The integrability of the systems is discussed in detail.
