Families of spherical surfaces and harmonic maps
Differential Geometry
2018-09-06 v2
Abstract
We study singularities of constant positive Gaussian curvature surfaces and determine the way they bifurcate in generic 1-parameter families of such surfaces. We construct the bifurcations explicitly using loop group methods. Constant Gaussian curvature surfaces correspond to harmonic maps, and we examine the relationship between the two types of maps and their singularities. Finally, we determine which finitely A-determined map-germs from the plane to the plane can be represented by harmonic maps.
Keywords
Cite
@article{arxiv.1709.00984,
title = {Families of spherical surfaces and harmonic maps},
author = {David Brander and Farid Tari},
journal= {arXiv preprint arXiv:1709.00984},
year = {2018}
}
Comments
30 pages, 7 figures. Version 2: substantial revision compared with version 1. The results are essentially the same, but some of the arguments are improved or corrected