The Generalized Liouville's Theorems via Euler-Lagrange Cohomology Groups on Symplectic Manifold

Han-Ying Guo, Jianzhong Pan, Bin Zhou

Based on the Euler-Lagrange cohomology groups $H_{EL}^{(2k-1)}({\mathcal{M}}^{2n})(1⩽k⩽n)$ on symplectic manifold $({\mathcal{M}}^{2n},\omega )$, their properties and a kind o…