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

Volume 114 / 2009

Qilin Yang Colloquium Mathematicum 114 (2009), 277-289 MSC: 53C43, 58E20. DOI: 10.4064/cm114-2-9


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.


  • Qilin YangMathematical Department
    Tsinghua University
    100084, Beijing
    P.R. China
    Graduate School of Mathematics
    Nagoya University Chikusa-ku
    Nagoya 464-8602, Japan

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