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(Reference retrieved automatically from Google Scholar through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

A topological minorization for the volume of vector fields on 5-manifolds

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Author(s):
Brito‚ F.G.B. ; Chacón‚ P.M.
Total Authors: 2
Document type: Journal article
Source: ARCHIV DER MATHEMATIK; v. 85, n. 3, p. 283-292, 2005.
Abstract

A vector field X on a Riemannian manifold M determines a submanifold in the tangent bundle. The volume of X is the volume of this submanifold for the induced Sasaki metric. When M is compact, the volume is well defined and, usually, this functional is studied for unit fields. Parallel vector fields are trivial minima of this functional. For manifolds of dimension 5, we obtain an explicit result showing how the topology of a vector field with constant length influences its volume. We apply this result to the case of vector fields that define Riemannian foliations with all leaves compact. (AU)

FAPESP's process: 99/02684-5 - Geometry and Topology of Riemannian Manifolds
Grantee:Fabiano Gustavo Braga Brito
Support Opportunities: Research Projects - Thematic Grants