Indefinite Affine Hyperspheres Admitting a Pointwise Symmetry. Part 2
An affine hypersurface M is said to admit a pointwise symmetry, if there exists a subgroup G of Aut(TpM) for all p ∈ M, which preserves (pointwise) the affine metric h, the difference tensor K and the affine shape operator S. Here, we consider 3-dimensional indefinite affine hyperspheres, i.e. S = H...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2009 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2009
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149115 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Indefinite Affine Hyperspheres Admitting a Pointwise Symmetry. Part 2 / C. Scharlach // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 14 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862699866747043840 |
|---|---|
| author | Scharlach, C. |
| author_facet | Scharlach, C. |
| citation_txt | Indefinite Affine Hyperspheres Admitting a Pointwise Symmetry. Part 2 / C. Scharlach // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 14 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | An affine hypersurface M is said to admit a pointwise symmetry, if there exists a subgroup G of Aut(TpM) for all p ∈ M, which preserves (pointwise) the affine metric h, the difference tensor K and the affine shape operator S. Here, we consider 3-dimensional indefinite affine hyperspheres, i.e. S = HId (and thus S is trivially preserved). In Part 1 we found the possible symmetry groups G and gave for each G a canonical form of K. We started a classification by showing that hyperspheres admitting a pointwise Z₂ × Z₂ resp. R-symmetry are well-known, they have constant sectional curvature and Pick invariant J < 0 resp. J = 0. Here, we continue with affine hyperspheres admitting a pointwise Z₃- or SO(2)-symmetry. They turn out to be warped products of affine spheres (Z₃) or quadrics (SO(2)) with a curve.
|
| first_indexed | 2025-12-07T16:37:12Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149115 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:37:12Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Scharlach, C. 2019-02-19T17:29:18Z 2019-02-19T17:29:18Z 2009 Indefinite Affine Hyperspheres Admitting a Pointwise Symmetry. Part 2 / C. Scharlach // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 14 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 53A15; 53B30 https://nasplib.isofts.kiev.ua/handle/123456789/149115 An affine hypersurface M is said to admit a pointwise symmetry, if there exists a subgroup G of Aut(TpM) for all p ∈ M, which preserves (pointwise) the affine metric h, the difference tensor K and the affine shape operator S. Here, we consider 3-dimensional indefinite affine hyperspheres, i.e. S = HId (and thus S is trivially preserved). In Part 1 we found the possible symmetry groups G and gave for each G a canonical form of K. We started a classification by showing that hyperspheres admitting a pointwise Z₂ × Z₂ resp. R-symmetry are well-known, they have constant sectional curvature and Pick invariant J < 0 resp. J = 0. Here, we continue with affine hyperspheres admitting a pointwise Z₃- or SO(2)-symmetry. They turn out to be warped products of affine spheres (Z₃) or quadrics (SO(2)) with a curve. This paper is a contribution to the Special Issue “Elie Cartan and Differential Geometry”. Partially supported by the DFG-Project PI 158/4-5 ‘Geometric Problems and Special PDEs’. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Indefinite Affine Hyperspheres Admitting a Pointwise Symmetry. Part 2 Article published earlier |
| spellingShingle | Indefinite Affine Hyperspheres Admitting a Pointwise Symmetry. Part 2 Scharlach, C. |
| title | Indefinite Affine Hyperspheres Admitting a Pointwise Symmetry. Part 2 |
| title_full | Indefinite Affine Hyperspheres Admitting a Pointwise Symmetry. Part 2 |
| title_fullStr | Indefinite Affine Hyperspheres Admitting a Pointwise Symmetry. Part 2 |
| title_full_unstemmed | Indefinite Affine Hyperspheres Admitting a Pointwise Symmetry. Part 2 |
| title_short | Indefinite Affine Hyperspheres Admitting a Pointwise Symmetry. Part 2 |
| title_sort | indefinite affine hyperspheres admitting a pointwise symmetry. part 2 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149115 |
| work_keys_str_mv | AT scharlachc indefiniteaffinehyperspheresadmittingapointwisesymmetrypart2 |