Affine hypersurfaces admitting a pointwise symmetry
| dc.creator | Lu, Ying | |
| dc.creator | Scharlach, Christine | |
| dc.date | 2005-10-07 | |
| dc.date.accessioned | 2026-07-07T06:47:13Z | |
| dc.date.available | 2026-07-07T06:47:13Z | |
| dc.description | An affine hypersurface is said to admit a pointwise symmetry, if there exists a subgroup of the automorphism group of the tangent space, which preserves (pointwise) the affine metric h, the difference tensor K and the affine shape operator S. In this paper, we deal with positive definite affine hypersurfaces of dimension three. First we solve an algebraic problem. We determine the non-trivial stabilizers G of the pair (K,S) under the action of SO(3) on an Euclidean vectorspace (V,h) and find a representative (canonical form of K and S) of each (SO(3)/G)-orbit. Then, we classify hypersurfaces admitting a pointwise G-symmetry for all non-trivial stabilizers G (apart of Z_2). Besides well-known hypersurfaces we obtain e.g. warped product structures of two-dimensional affine spheres (resp. quadrics) and curves. | |
| dc.description | 27 pages, AMSTeX, submitted to Results in Math | |
| dc.identifier | https://arxiv.org/abs/math/0510150 | |
| dc.identifier | http://arxiv.org/abs/math/0510150 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103584 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53A15 (primary), 15A21 (secondary) | |
| dc.title | Affine hypersurfaces admitting a pointwise symmetry | |
| dc.type | text |