中文摘要：

研究了Lorentzian乘积空间Mn（c） ×R1中具有平行平均曲率向量的双调和类空子流形.首先,证明了一般伪黎曼空间中具有平行平均曲率向量的双调和类空子流形的一个不变方程,然后利用该方程得到了Lorentzian乘积空间Mn（c）×R1中类空子流形是双调和的充要条件,并得到了这类子流形极小的充分条件.此外,还证明了一个关于Lorentzian乘积空间Mn（c）×R1中双调和类空超曲面的不存在性结果.

英文摘要：

We study biharmonic spacelike submanifolds in certain Lorent product spaces with parallel mean curvature vector field. We first prove an invariant biharmonic equation for such submanifolds in general pseudo-Ri- emannian manifolds, then we apply it to Lorentzian product manifoldsM n （c） × R1 , and obtain a sufficient and necessary condition for spacelike submanifolds and some sufficient conditions for such submanifolds to be minimal ones. Also, we prove a nonexistence result for biharmonic hypersurfaces which can be viewed as the dual of their Riemannian version.