In this paper, the structure of Jacobi vector fields on warped product manifolds is investigated. Many characterizations of Jacobi vector fields on warped product manifolds are obtained. Consequently, conjugate points on warped product manifolds are also considered. Finally, we apply our results to characterize conjugate points of some well-known warped product spacetimes.

中文翻译：

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翘曲积流形上的雅可比向量场和共轭点

本文研究了翘曲积流形上的雅可比向量场的结构。获得了翘曲乘积流形上雅可比矢量场的许多表征。因此，还考虑了翘曲乘积流形上的共轭点。最后，我们应用我们的结果来表征一些众所周知的扭曲乘积时空的共轭点。