有关两类辛超流形上的辛向量场

Symplectic Vector Fields on Two Types of Special Symplectic Supermanifolds

该文在（0，n）的维辛超流形M=（e，A）的左A模DerA上定义了算子η，给出了M上的向量场为辛向量场的两个充要条件，并得到了算子η的一些恒等式．此外，还给了余切超流形T^＊（M）=（e，S（DerA））上辛向量场的三个判定条件，并证明了它们的等价性．

In this paper, an operator U is defined in the left A module DerA on symplectic supermanifold M=（e, A） of dimension （0, n）. Two sufficient and necessary conditions are given for vector fields on M being symplectic vecter fields, and some identities about the operator η are obtianed. Futrthermore, three decision conditions are given to judge symplectic vector fields on cotangent supermanifold T＊（M） = （e, S（DerA））, and their equivalences are proved.