Space-like Submanifolds with Parallel Normalized Mean Curvature Vector Field in de Sitter Space
Space-like submanifolds, with dimension greater than three and with negative definite normal bundle in a general de Sitter space, of any index, are studied. For the compact space-like submanifolds whose mean curvature has no zero and the corresponding normalized vector field is parallel, under natur...
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| Published in: | Журнал математической физики, анализа, геометрии |
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| Date: | 2011 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2011
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/106689 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Space-like Submanifolds with Parallel Normalized Mean Curvature Vector Field in de Sitter Space / Sh. Shu // Журнал математической физики, анализа, геометрии. — 2011. — Т. 7, № 4. — С. 352-369. — Бібліогр.: 22 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862728924443705344 |
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| author | Shu, Sh. |
| author_facet | Shu, Sh. |
| citation_txt | Space-like Submanifolds with Parallel Normalized Mean Curvature Vector Field in de Sitter Space / Sh. Shu // Журнал математической физики, анализа, геометрии. — 2011. — Т. 7, № 4. — С. 352-369. — Бібліогр.: 22 назв. — англ. |
| collection | DSpace DC |
| container_title | Журнал математической физики, анализа, геометрии |
| description | Space-like submanifolds, with dimension greater than three and with negative definite normal bundle in a general de Sitter space, of any index, are studied. For the compact space-like submanifolds whose mean curvature has no zero and the corresponding normalized vector field is parallel, under natural boundedness assumptions on the lengths of the gradient of the length of the mean curvature and the covariant derivative of the second fundamental form, it is proved that they must be totally umbilical. As an application, two characterizations of totally umbilical space-like submanifolds in terms of the scalar curvature and the length of its second fundamental form are given. All the results extend the previous ones obtained by Liu for the case of space-like hypersurfaces in de Sitter space of index one. In addition, for the complete space-like submanifolds, whose normalized mean curvature vector field is parallel, two characterizations of totally umbilical space-like submanifolds and hyperbolic cylinders are obtained.
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| first_indexed | 2025-12-07T19:11:29Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-106689 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-12-07T19:11:29Z |
| publishDate | 2011 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Shu, Sh. 2016-10-02T20:20:43Z 2016-10-02T20:20:43Z 2011 Space-like Submanifolds with Parallel Normalized Mean Curvature Vector Field in de Sitter Space / Sh. Shu // Журнал математической физики, анализа, геометрии. — 2011. — Т. 7, № 4. — С. 352-369. — Бібліогр.: 22 назв. — англ. 1812-9471 https://nasplib.isofts.kiev.ua/handle/123456789/106689 Space-like submanifolds, with dimension greater than three and with negative definite normal bundle in a general de Sitter space, of any index, are studied. For the compact space-like submanifolds whose mean curvature has no zero and the corresponding normalized vector field is parallel, under natural boundedness assumptions on the lengths of the gradient of the length of the mean curvature and the covariant derivative of the second fundamental form, it is proved that they must be totally umbilical. As an application, two characterizations of totally umbilical space-like submanifolds in terms of the scalar curvature and the length of its second fundamental form are given. All the results extend the previous ones obtained by Liu for the case of space-like hypersurfaces in de Sitter space of index one. In addition, for the complete space-like submanifolds, whose normalized mean curvature vector field is parallel, two characterizations of totally umbilical space-like submanifolds and hyperbolic cylinders are obtained. The author would like to thank the referee for his/her careful reading of the original manuscript and for making many valuable suggestions and comments that have signi¯cantly improved the paper. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии Space-like Submanifolds with Parallel Normalized Mean Curvature Vector Field in de Sitter Space Article published earlier |
| spellingShingle | Space-like Submanifolds with Parallel Normalized Mean Curvature Vector Field in de Sitter Space Shu, Sh. |
| title | Space-like Submanifolds with Parallel Normalized Mean Curvature Vector Field in de Sitter Space |
| title_full | Space-like Submanifolds with Parallel Normalized Mean Curvature Vector Field in de Sitter Space |
| title_fullStr | Space-like Submanifolds with Parallel Normalized Mean Curvature Vector Field in de Sitter Space |
| title_full_unstemmed | Space-like Submanifolds with Parallel Normalized Mean Curvature Vector Field in de Sitter Space |
| title_short | Space-like Submanifolds with Parallel Normalized Mean Curvature Vector Field in de Sitter Space |
| title_sort | space-like submanifolds with parallel normalized mean curvature vector field in de sitter space |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/106689 |
| work_keys_str_mv | AT shush spacelikesubmanifoldswithparallelnormalizedmeancurvaturevectorfieldindesitterspace |