On The Geometry Of Submanifolds In Certain Warped Products

In this paper, we deal with n-dimensional submanifolds immersed in a slab of a warped product of the type I x (rho) Mn+p-1. Under suitable constraints on the warping function rho and assuming that such a submanifold Sigma(n) is either complete or stochastically complete, we apply some maximum principles in order to show that Sigma(n) must be contained in a slice of I x (rho) Mn+p-1. In particular, from our results we guarantee the nonexistence of n-dimensional closed minimal submanifolds immersed in R-m x Hn+1. Furthermore, we construct a nontrivial duo-graph in R x H( )(2)x R which illustrates the importance of our rigidity results.