Geodesic
Harmonic maps from compact Kähler manifolds with positive scalar curvature to Kähler manifolds of strongly seminegative curvature
Qilin Yang1
1 Mathematical Department Tsinghua University 100084, Beijing P.R. China and Graduate School of Mathematics Nagoya University Chikusa-ku Nagoya 464-8602, Japan
Colloquium Mathematicum, Tome 114 (2009) no. 2, pp. 277-289 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm114-2-9
Keywords: known there non constant harmonic map closed riemannian manifold positive ricci curvature complete riemannian manifold non positive sectional curvature reduces assumption ricci curvature scalar curvature vanishing theorem does general raises question what information obtain existence non constant harmonic map paper gives answer problem manifolds hler results obtained optimal

Qilin Yang 1

1 Mathematical Department Tsinghua University 100084, Beijing P.R. China and Graduate School of Mathematics Nagoya University Chikusa-ku Nagoya 464-8602, Japan 
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     title = {Harmonic maps from compact {K\"ahler} manifolds with
 positive scalar curvature  to {K\"ahler} manifolds
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     journal = {Colloquium Mathematicum},
     pages = {277--289},
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Qilin Yang. Harmonic maps from compact Kähler manifolds with
 positive scalar curvature  to Kähler manifolds
 of strongly seminegative curvature. Colloquium Mathematicum, Tome 114 (2009) no. 2, pp. 277-289. doi: 10.4064/cm114-2-9

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