Quasi-homogeneous domains and convex affine manifolds
| dc.creator | Jo, Kyeonghee | |
| dc.date | 2003-05-01 | |
| dc.date.accessioned | 2026-07-07T04:57:40Z | |
| dc.date.available | 2026-07-07T04:57:40Z | |
| dc.description | In this article, we study convex affine domains which can cover a compact affine manifold. For this purpose, we first show that every strictly convex quasi-homogeneous projective domain has at least $C^1$ boundary and it is an ellipsoid if its boundary is twice differentiable. And then we show that an n-dimensional paraboloid is the only strictly convex quasi-homogeneous affine domain in $\mathbb R^n$ up to affine equivalence. Furthermore we prove that if a strictly convex quasi-homogeneous projective domain is $C^α$ on an open subset of its boundary, then it is $C^α$ everywhere. Using this fact and the properties of asymptotic cones we find all possible shapes for developing images of compact convex affine manifolds with dimension $\leq 4$. | |
| dc.description | 21 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/math/0305027 | |
| dc.identifier | http://arxiv.org/abs/math/0305027 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67343 | |
| dc.subject | Geometric Topology | |
| dc.subject | 52A20; 57M50 | |
| dc.title | Quasi-homogeneous domains and convex affine manifolds | |
| dc.type | text |