3-dimensional affine hypersurfaces admitting a pointwise SO(2)- or Z_3-symmetry
| dc.creator | Scharlach, Christine | |
| dc.creator | Vrancken, Luc | |
| dc.date | 2003-03-07 | |
| dc.date.accessioned | 2026-07-07T04:55:52Z | |
| dc.date.available | 2026-07-07T04:55:52Z | |
| dc.description | In (equi-)affine differential geometry, the most important algebraic invariants are the affine (Blaschke) metric h, the affine shape operator S and the difference tensor K. A hypersurface is said to admit a pointwise symmetry if at every point there exists a linear transformation preserving the affine metric, the affine shape operator and the difference tensor K. The study of submanifolds which admit pointwise isometries was initiated by Bryant (math.DG/0007128). In this paper, we consider the 3-dimensional positive definite hypersurfaces for which at each point the group of symmetries is isomorphic to either Z_3 or SO(2). We classify such hypersurfaces and show how they can be constructed starting from 2-dimensional positive definite affine spheres. | |
| dc.description | 22 pages, preprint from Oct. 7, 2002 | |
| dc.identifier | https://arxiv.org/abs/math/0303099 | |
| dc.identifier | http://arxiv.org/abs/math/0303099 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66732 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53A15 | |
| dc.title | 3-dimensional affine hypersurfaces admitting a pointwise SO(2)- or Z_3-symmetry | |
| dc.type | text |