Harmonic maps and sections on spheres
Differential Geometry
2007-05-23 v1
Abstract
The absence of interesting harmonic sections for the Sasaki and Cheeger-Gromoll metrics has led to the consideration of alternatives, for example in the form of a two-parameter family of natural metrics shown to relax existence conditions for harmonicity. This article investigates harmonic Killing vector fields, proves their non-existence on S^2, obtains rigidity results for harmonic gradient vector fields on the two-sphere, classifies spherical quadratic gradient fields in all dimensions and determines the tension field, concluding with the discovery of a family of metrics making Hopf vector fields harmonic maps on S^{2n+1}.
Keywords
Cite
@article{arxiv.math/0703060,
title = {Harmonic maps and sections on spheres},
author = {M. Benyounes and E. Loubeau and C. M. Wood},
journal= {arXiv preprint arXiv:math/0703060},
year = {2007}
}
Comments
A detailed version is available at: http://maths2.univ-brest.fr/~loubeau/articles/harm-long.pdf