Geometrical versus Topological Properties of Manifolds
| dc.creator | Matheus, Carlos | |
| dc.creator | Oliveira, Krerley | |
| dc.date | 2003-07-04 | |
| dc.date | 2005-11-19 | |
| dc.date.accessioned | 2026-07-07T06:35:40Z | |
| dc.date.available | 2026-07-07T06:35:40Z | |
| dc.description | Given a compact $n$-dimensional immersed Riemannian manifold $M^n$ in some Euclidean space we prove that if the Hausdorff dimension of the singular set of the Gauss map is small, then $M^n$ is homeomorphic to the sphere $S^n$. Also, we define a concept of finite geometrical type and prove that finite geometrical type hypersurfaces with small set of points of zero Gauss-Kronecker curvature are topologically the sphere minus a finite number of points. A characterization of the $2n$-catenoid is obtained. | |
| dc.identifier | https://arxiv.org/abs/math/0307070 | |
| dc.identifier | http://arxiv.org/abs/math/0307070 | |
| dc.identifier | Journal of the Institute of Mathematics of Jussieu, vol. 4, n. 4, p. 630-651, 2005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99864 | |
| dc.subject | Differential Geometry | |
| dc.title | Geometrical versus Topological Properties of Manifolds | |
| dc.type | text |