On the index of harmonic maps from surfaces to complex projective spaces
Differential Geometry
2020-03-05 v3
Abstract
We estimate the dimensions of the spaces of holomorphic sections of certain line bundles to give improved lower bounds on the index of complex isotropic harmonic maps to complex projective space from the sphere and torus, and in some cases from higher genus surfaces.
Cite
@article{arxiv.1901.11475,
title = {On the index of harmonic maps from surfaces to complex projective spaces},
author = {Joe Oliver},
journal= {arXiv preprint arXiv:1901.11475},
year = {2020}
}
Comments
We have added examples for each genus for which our estimates for the index improve those of Eells and Wood