超Killing方程与超对称变换

在超空间(x,θ)上定义了度规张量场G^AB后,计算了四阶曲率张量R^D_ABC并找出其推广的循环性(cyclicity)。推导了超空间上保度量变换所应满足的条件,即超Killing方程:ξ_A:B+η_abξ_B:A=0。在零曲率情形,求出了超Killing方程的通解,及其相应生成元间的对易关系。在常曲率情形,找出了超Killing方程的特解。 关键词：

SUPER KILLING EQUATION AND SUPERSYM-METRY TRANSFORMATION

In super space (x, θ), as the metric tensor field G^AB(x, θ) is given, we calculated the Riemann curvature tensor R^D_ABC of fourth rank and its generalized cyclicity.The equation that must be satisfied by isometry in the super space, i.e. super Killing equation: ξ_A:B+η_abξ_B:A=0, is deduced.In flat super space with zero curvature tensor, we have obtained the general solu-tions of the super Killing equation and the commutation relations of the corresponding generators. In the case of constant curvature, we have obtained a special solution of the super Killing equation.