Harmonic maps from compact Kähler manifolds with positive scalar curvature to Kähler manifolds of strongly seminegative curvature

Qilin Yang. "Harmonic maps from compact Kähler manifolds with positive scalar curvature to Kähler manifolds of strongly seminegative curvature." Colloquium Mathematicae 114.2 (2009): 277-289. <http://eudml.org/doc/284370>.

@article{QilinYang2009,
abstract = {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.},
author = {Qilin Yang},
journal = {Colloquium Mathematicae},
keywords = {harmonic map; Kähler manifold; strongly seminegative curvature},
language = {eng},
number = {2},
pages = {277-289},
title = {Harmonic maps from compact Kähler manifolds with positive scalar curvature to Kähler manifolds of strongly seminegative curvature},
url = {http://eudml.org/doc/284370},
volume = {114},
year = {2009},
}

TY - JOUR
AU - Qilin Yang
TI - Harmonic maps from compact Kähler manifolds with positive scalar curvature to Kähler manifolds of strongly seminegative curvature
JO - Colloquium Mathematicae
PY - 2009
VL - 114
IS - 2
SP - 277
EP - 289
AB - 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.
LA - eng
KW - harmonic map; Kähler manifold; strongly seminegative curvature
UR - http://eudml.org/doc/284370
ER -