6533b82bfe1ef96bd128d5c4

RESEARCH PRODUCT

Harmonicity and minimality of oriented distributions

Lieven VanheckeOlga Gil-medranoJc Gonzalez-davila

subject

General MathematicsBundleMathematical analysisImmersion (mathematics)Pushforward (differential)Harmonic mapTangentMathematics::Differential GeometryHopf fibrationExponential map (Riemannian geometry)Mathematics

description

We consider an oriented distribution as a section of the corresponding Grassmann bundle and, by computing the tension of this map for conveniently chosen metrics, we obtain the conditions which the distribution must satisfy in order to be critical for the functionals related to the volume or the energy of the map. We show that the three-dimensional distribution ofS4m+3 tangent to the quaternionic Hopf fibration defines a harmonic map and a minimal immersion and we extend these results to more general situations coming from 3-Sasakian and quaternionic geometry.

yearjournalcountryeditionlanguage
2004-12-01Israel Journal of Mathematics
https://doi.org/10.1007/bf02803502