Indefinite Affine Hyperspheres Admitting a Pointwise Symmetry. Part 2
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Indefinite Affine Hyperspheres Admitting a Pointwise Symmetry. Part 2
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| Creator |
Scharlach, C.
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| 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.
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| Date |
2019-02-19T17:29:18Z
2019-02-19T17:29:18Z 2009 |
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| Type |
Article
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| Identifier |
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 http://dspace.nbuv.gov.ua/handle/123456789/149115 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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