Geometry and topology under positive/nonnegative sectional curvature
Biharmonic surfaces in three-dimensional Riemannian manifolds
| Full text | |
| Author(s): |
Brito‚ F.B.
;
Chacón‚ P.M.
;
Naveira‚ AM
Total Authors: 3
|
| Document type: | Journal article |
| Source: | COMMENTARII MATHEMATICI HELVETICI; v. 79, n. 2, p. 300-316, 2004. |
| Abstract | |
A unit vector field X on a Riemannian manifold determines a submanifold in the unit tangent bundle. The volume of X is the volume of this submanifold for the induced Sasaki metric. It is known that the parallel fields are the trivial minima. In this paper, we obtain a lower bound for the volume in terms of the integrals of the 2i-symmetric functions of the second fundamental form of the orthogonal distribution to the field X. In the spheres S2k+1, this lower bound is independent of X. Consequently, the volume of a unit vector field on an odd-sphere is always greater than the volume of the radial field. The main theorem on volumes is applied also to hyperbolic compact spaces, giving a non-trivial lower bound of the volume of unit fields. (AU) | |
| FAPESP's process: | 99/02684-5 - Geometry and Topology of Riemannian Manifolds |
| Grantee: | Fabiano Gustavo Braga Brito |
| Support Opportunities: | Research Projects - Thematic Grants |