Abstract: The symplectic geometry characterization of second order singular J- symmetric differential operators was investigated. By constructing different quotient spaces, self-adjoint extensions of second order J- symmetric differential operators were studied using the method of symplectic geometry. Then classification and description of complete J-Lagrangian submanifold corresponding with self-adjoint domains of second order differential operators were obtained.

Key words: Differential operators, J-Symplectic spaces, J-Lagrangian submanifold

摘要： 研究了二阶奇型J-对称微分算子辛几何刻画问题,通过构造商空间，应用辛几何的方法讨论了二阶J-对称微分算子的自共轭扩张问题。给出了与二阶微分算子自共轭域相对应的完全J-Lagrangian子流型的分类与描述。

关键词: 微分算子, J-辛空间, J-Lagrangian子流型