0000000000726711

AUTHOR

Pablo M. Chacón

showing 2 related works from this author

On the volume of unit vector fields on spaces of constant sectional curvature

2004

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.

Parallelizable manifoldGeneral MathematicsGEOMETRIA RIEMANNIANAMathematical analysisRiemannian manifoldSubmanifoldNormal bundleUnit tangent bundleMathematics::Differential GeometrySectional curvatureMathematics::Symplectic GeometryTangential and normal componentsTubular neighborhoodMathematics
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On the Energy of Distributions, with Application to the Quaternionic Hopf Fibrations

2001

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.

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 functionalMathematicsMonatshefte für Mathematik
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