Relationship between volume and energy of vector fields
By O. Gil-Medrano. 2001
78 citations recorded by the source corpus.
Abstract A unified study of energy and volume functionals is presented here by determining the critical points of a functional that extends simultaneously energy and volume and that is defined on the product of the manifold of smooth maps C∞(M,N) times the manifold M of riemannian metrics on M. The restriction of this functional to different submanifolds of the space of vector fields X (M)× M is also considered, and used to study several functionals generalizing volume and energy or total bending of vector fields
Subfields: Applied Mathematics, Astronomy and Astrophysics
View Paper: https://www.semanticscholar.org/paper/d170eb023a3eb7337f4f99b43867ff12bcfa6e9e
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In Applied Mathematics
In Astronomy and Astrophysics
Citations in the corpus
- The harmonicity of the Reeb vector field on contact metric 3-manifolds (2008, unknown): “V is a harmonic vector field if and only if the 1-form νV defined by νV (X) = tr(Z 7→ (∇Z AV )X), vanishes on V , that is, on the distribution determined by tangent vectors orthogonal to V ; see [Wiegmink 1995; Wood 1997; Gil-Medrano 2001].”
- Second variation of volume and energy of vector fields. Stability of Hopf vector fields (2001, methodology): “Nevertheless, as it has been shown in [ GM2 ], for a critical point V of E to determine a harmonic map, it is necessary to fullfil certain curvature condition.”