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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| Видавець: | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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| Дата: | 2011 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2011
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| Назва видання: | Журнал математической физики, анализа, геометрии |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/106689 |
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| Цитувати: | 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. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-106689 |
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dspace |
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irk-123456789-1066892016-10-03T03:02:21Z Space-like Submanifolds with Parallel Normalized Mean Curvature Vector Field in de Sitter Space Shu, Sh. 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. 2011 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/106689 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Shu, Sh. |
| spellingShingle |
Shu, Sh. Space-like Submanifolds with Parallel Normalized Mean Curvature Vector Field in de Sitter Space Журнал математической физики, анализа, геометрии |
| author_facet |
Shu, Sh. |
| author_sort |
Shu, Sh. |
| title |
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_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_sort |
space-like submanifolds with parallel normalized mean curvature vector field in de sitter space |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/106689 |
| 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. |
| series |
Журнал математической физики, анализа, геометрии |
| work_keys_str_mv |
AT shush spacelikesubmanifoldswithparallelnormalizedmeancurvaturevectorfieldindesitterspace |
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2023-10-18T20:13:30Z |
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2023-10-18T20:13:30Z |
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1796149300030341120 |