The study of warped products plays versatile roles in differential geometry as well as in mathematical physics, especially in general relativity $(GR)$. In the present paper, we study statistical submanifolds in a statistical warped product with some related examples. For such submanifolds, we establish a Chen's first inequality and also discuss the equality case. Finally, we study the statistical warped product immersions and obtain some results.

中文翻译：

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统计翘曲积流形的子流形的陈第一不等式

翘曲积的研究在微分几何和数学物理中，尤其是在广义相对论中扮演着广泛的角色 $(G\mathrm{电阻})$. 在本文中，我们通过一些相关示例研究了统计扭曲产品中的统计子流形。对于这样的子流形，我们建立了 Chen 的第一个不等式，并讨论了等式的情况。最后，我们研究了统计翘曲产品浸入并获得了一些结果。