In this paper, we deal with n-dimensional submanifolds immersed in a slab of a warped product of the type I ×ρMn+p−1. Under suitable constraints on the warping function ρ and assuming that such a submanifold Σn is either complete or stochastically complete, we apply some maximum principles in order to show that Σn must be contained in a slice of I ×ρMn+p−1. In particular, from our results we guarantee the nonexistence of n-dimensional closed minimal submanifolds immersed in ℝm × ℍn+1. Furthermore, we construct a nontrivial duo-graph in ℝ × ℍ2 × ℝ which illustrates the importance of our rigidity results.

中文翻译：

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关于某些翘曲产品中子流形的几何形状

在本文中，我们处理n浸没在翘曲产品板中的维子流形一世 ×ρ米n+p-1. 在对翘曲函数的适当约束下ρ并假设这样的子流形Σn是完整的或随机完整的，我们应用一些最大原则来证明Σn必须包含在切片中一世 ×ρ米n+p-1. 特别是，根据我们的结果，我们保证不存在n维封闭最小子流形ℝ米 × ℍn+1. 此外，我们在ℝ × ℍ2 × ℝ这说明了我们刚性结果的重要性。