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On the geometry of submanifolds in certain warped products
International Journal of Mathematics ( IF 0.6 ) Pub Date : 2021-04-23 , DOI: 10.1142/s0129167x21500440
Jogli G. Araújo 1 , Henrique F. de Lima 2 , Eraldo A. Lima 3 , Márcio S. Santos 3
Affiliation  

In this paper, we deal with n-dimensional submanifolds immersed in a slab of a warped product of the type I ×ρMn+p1. 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+p1. In particular, from our results we guarantee the nonexistence of n-dimensional closed minimal submanifolds immersed in m × n+1. Furthermore, we construct a nontrivial duo-graph in × 2 × which illustrates the importance of our rigidity results.

中文翻译:

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 ×ρn+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 ×ρn+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 × n+1. 此外,我们在 × 2 × 这说明了我们刚性结果的重要性。
更新日期:2021-04-23
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