$ϕ$-parabolicity and the uniqueness of spacelike hypersurfaces immersed in a spatially weighted GRW spacetime
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| Main Authors: | , , , |
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| Format: | Preprint |
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2016
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| _version_ | 1866929235272138752 |
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| author | Albujer, Alma L. de Lima, Henrique F. Oliveira, Arlandson M. Velásquez, Marco Antonio L. |
| author_facet | Albujer, Alma L. de Lima, Henrique F. Oliveira, Arlandson M. Velásquez, Marco Antonio L. |
| contents | In this paper, we extend a technique due to Romero, Rubio and Salamanca establishing sufficient conditions to guarantee the parabolicity of complete spacelike hypersurfaces immersed in a weighted generalized Robertson-Walker spacetime whose fiber has phi-parabolic universal Riemannian covering. As some applications of this criteria, we obtain uniqueness results concerning spacelikes hypersurfaces immersed in spatially weighted generalized Robertson-Walker spacetimes. Furthermore, Calabi-Bernstein type results are also given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1604_04126 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | $ϕ$-parabolicity and the uniqueness of spacelike hypersurfaces immersed in a spatially weighted GRW spacetime Albujer, Alma L. de Lima, Henrique F. Oliveira, Arlandson M. Velásquez, Marco Antonio L. Differential Geometry Primary 53C42, 53A07, Secondary 35P15 In this paper, we extend a technique due to Romero, Rubio and Salamanca establishing sufficient conditions to guarantee the parabolicity of complete spacelike hypersurfaces immersed in a weighted generalized Robertson-Walker spacetime whose fiber has phi-parabolic universal Riemannian covering. As some applications of this criteria, we obtain uniqueness results concerning spacelikes hypersurfaces immersed in spatially weighted generalized Robertson-Walker spacetimes. Furthermore, Calabi-Bernstein type results are also given. |
| title | $ϕ$-parabolicity and the uniqueness of spacelike hypersurfaces immersed in a spatially weighted GRW spacetime |
| topic | Differential Geometry Primary 53C42, 53A07, Secondary 35P15 |
| url | https://arxiv.org/abs/1604.04126 |