Harmonic maps from compact Kähler manifolds with positive scalar curvature to Kähler manifolds of strongly seminegative curvature
Harmonic maps from compact Kähler manifolds with positive scalar curvature to Kähler manifolds of strongly seminegative curvature
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DOI：
10.4064/cm114-2-9
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发表时间：
2009
影响因子：
0.4
通讯作者：
Qilin Yang
中科院分区：
文献类型：
--
作者：
Qilin Yang
从正Ricci曲率的闭黎曼流形到非正截面曲率的完备黎曼流形不存在非常数调和映射。如果把关于里奇曲率的假设简化为关于标量曲率的假设，那么这样的消失定理一般不成立。这就提出了一个问题：我们可以从非常数调和映射的存在性中获得什么信息？当两个流形都是Kähler流形时，本文给出了这个问题的一个答案，所得结果是最优的。
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.