On the geometry of submanifolds in certain warped products
Keyword(s):
In this paper, we deal with [Formula: see text]-dimensional submanifolds immersed in a slab of a warped product of the type [Formula: see text]. Under suitable constraints on the warping function [Formula: see text] and assuming that such a submanifold [Formula: see text] is either complete or stochastically complete, we apply some maximum principles in order to show that [Formula: see text] must be contained in a slice of [Formula: see text]. In particular, from our results we guarantee the nonexistence of [Formula: see text]-dimensional closed minimal submanifolds immersed in [Formula: see text]. Furthermore, we construct a nontrivial duo-graph in [Formula: see text] which illustrates the importance of our rigidity results.
2002 ◽
Vol 45
(3)
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pp. 579-587
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Keyword(s):
2017 ◽
Vol 10
(04)
◽
pp. 1750067
Magnetic trajectories corresponding to Killing magnetic fields in a three-dimensional warped product
2020 ◽
Vol 17
(14)
◽
pp. 2050212
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