Integrability of generalized pluriharmonic maps
Integrability of generalized pluriharmonic maps
复制标题
广义多调和映射的可积性
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
L. Schafer
中科院分区：
文献类型：
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作者：
L. Schafer
本文给出了从几乎复域到伪黎曼对称目标的映射的例子，这些目标是多重调和的，也就是不可积的，即不允许有一个相联族。更准确地说，对于一类例子，源具有不可积的复结构，例如，近似Kähler结构，目标是黎曼对称空间，而对于另一类，源是复流形，目标是伪黎曼对称空间。这些例子表明，文献[12]中关于伴生族存在的一个结果，即定理5.3是尖锐的。
In this paper we provide examples of maps from almost complex domains into pseudo-Riemannian symmetric targets, which are pluriharmonic and not integrable, i.e. do not admit an associated family. More precisely, for one class of examples the source has a non-integrable complex structure, like for instance a nearly Kähler structure and the target is a Riemannian symmetric space and for the other class the source is a complex manifold and the target is a pseudo-Riemannian symmetric space. These examples show, that a former result, Theorem 5.3 of [12], on the existence of associated families is sharp.