It is well known there is no non-constant harmonic map from a closed Riemannian manifold of positive Ricci curvature to a complete Riemannian manifold with non-positive sectional curvature. If one reduces the assumption on the Ricci curvature to one on the scalar curvature, such a vanishing theorem does not hold in general. This raises the question: What information can we obtain from the existence of a non-constant harmonic map? This paper gives an answer to this problem when both manifolds are Kähler; the results obtained are optimal.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm114-2-9,
author = {Qilin Yang},
title = {Harmonic maps from compact K\"ahler manifolds with positive scalar curvature to K\"ahler manifolds of strongly seminegative curvature},
journal = {Colloquium Mathematicae},
volume = {116},
year = {2009},
pages = {277-289},
zbl = {1163.53040},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm114-2-9}
}
Qilin Yang. Harmonic maps from compact Kähler manifolds with positive scalar curvature to Kähler manifolds of strongly seminegative curvature. Colloquium Mathematicae, Tome 116 (2009) pp. 277-289. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm114-2-9/