Article
| Title: | Revisiting linear Weingarten spacelike submanifolds immersed in a locally symmetric semi-Riemannian space (English) |
| Author: | Barboza, Weiller F. C. |
| Author: | de Lima, Henrique F. |
| Author: | Velásquez, Marco A. L. |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 64 |
| Issue: | 1 |
| Year: | 2023 |
| Pages: | 39-61 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | In this paper, we deal with $n$-dimensional complete linear Weingarten spacelike submanifolds immersed with parallel normalized mean curvature vector field and flat normal bundle in a locally symmetric semi-Riemannian space $L_{p}^{n+p}$ of index $p>1$, which obeys some curvature constraints (such an ambient space can be regarded as an extension of a semi-Riemannian space form). Under appropriate hypothesis, we are able to prove that such a spacelike submanifold is either totally umbilical or isometric to an isoparametric submanifold of the ambient space. For this, we use three main core analytical tools: a suitable version of the Omori--Yau maximum principle, parabolicity with respect to a modified Cheng--Yau operator and a certain integrability property. (English) |
| Keyword: | locally symmetric semi-Riemannian space |
| Keyword: | mean curvature vector field |
| Keyword: | complete linear Weingarten spacelike submanifold |
| Keyword: | totally umbilical submanifold |
| Keyword: | isoparametric submanifold |
| Keyword: | $\mathcal L$-parabolicity |
| MSC: | 53C21 |
| MSC: | 53C42 |
| MSC: | 53C50 |
| idZBL: | Zbl 07790581 |
| idMR: | MR4631789 |
| DOI: | 10.14712/1213-7243.2023.013 |
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| Date available: | 2023-08-28T09:42:27Z |
| Last updated: | 2024-02-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151807 |
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