Morse theory and infinite families of harmonic maps between spheres
Abstract
Existence of an infinite sequence of harmonic maps between spheres of certain dimensions was proven by Bizon and Chmaj. This sequence shares many features of the BartnikMcKinnon sequence of solutions to the EinsteinYangMills equations as well as sequences of solutions that have arisen in other physical models. We apply Morse theory methods to prove existence of the harmonic map sequence and to prove certain index and convergence properties of this sequence. In addition, we generalize the result of Bizon and Chmaj to produce infinite sequences of harmonic maps not previously known. The key features ``responsible'' for the existence and properties of these sequences are thereby seen to be the presence of a reflection symmetry and the existence of a singular harmonic map of infinite index which is invariant under this symmetry.
 Publication:

arXiv eprints
 Pub Date:
 December 1999
 arXiv:
 arXiv:mathph/9912001
 Bibcode:
 1999math.ph..12001C
 Keywords:

 Mathematical Physics;
 Differential Geometry;
 58E20;
 83C20
 EPrint:
 17 pages, LaTeX