| Full text | |
| Author(s): |
Brito‚ F.
;
Johnson‚ D.L.
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Geometriae Dedicata; v. 109, n. 1, p. 253-267, 2004. |
| Abstract | |
The volume of a k-dimensional foliation F in a Riemannian manifold W is defined as the mass of the image of the Gauss map, which is a map from M to the Grassmann bundle of k-planes in the tangent bundle. Generalizing the construction by Gluck and Ziller (Comment. Math. Helv. 61 (1986), 177-192), 'singular' foliations by 3-spheres are constructed on round spheres S4n+3, as well as a singular foliation by 7-spheres on S-15, which minimize volume within their respective relative homology classes. These singular examples, even though they are not homologous to the graph of a foliation, provide lower bounds for volumes of regular three-dimensional foliations of S4n+3 and regular seven-dimensional foliations of S-15, since the double of these currents will be homologous to twice the graph of any smooth foliation by 3-manifolds. (AU) | |
| FAPESP's process: | 99/02684-5 - Geometry and Topology of Riemannian Manifolds |
| Grantee: | Fabiano Gustavo Braga Brito |
| Support Opportunities: | Research Projects - Thematic Grants |