6533b85bfe1ef96bd12bb3d1
RESEARCH PRODUCT
On the Energy of Distributions, with Application to the Quaternionic Hopf Fibrations
Pablo M. ChacónJane M. WestonAntonio Martínez Naveirasubject
Pure mathematicsGeneral MathematicsMathematical analysisCritical point (mathematics)law.inventionSection (fiber bundle)Mathematics::Algebraic GeometrylawGrassmannianSPHERESMathematics::Differential GeometryMathematics::Symplectic GeometryManifold (fluid mechanics)Energy (signal processing)Distribution (differential geometry)Energy functionalMathematicsdescription
The energy of an oriented q-distribution ? in a compact oriented manifold M is defined to be the energy of the section of the Grassmannian manifold of oriented q-planes in M induced by ?. In the Grassmannian, the Sasaki metric is considered. We show here a condition for a distribution to be a critical point of the energy functional. In the spheres, we see that Hopf fibrations \(\) are critical points. Later, we prove the instability for these fibrations.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2001-10-01 | Monatshefte für Mathematik |