On the existence of balanced and SKT metrics on nilmanifolds
On the existence of balanced and SKT metrics on nilmanifolds
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关于 nilmanifolds 上平衡和 SKT 度量的存在性
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Luigi Vezzoni
中科院分区：
文献类型：
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作者：
A. Fino;Luigi Vezzoni
在复流形上，同时是SKT和平衡的厄米特度量必然是K“ahler的。证明了：如果紧致复流形（M，J）有一个SKT度量和一个平衡度量都与J相容，则（M，J）必是K“ahler.我们证明了该猜想对nilmanifold是成立的。
On a complex manifold an Hermitian metric which is simultaneously SKT and balanced has to be necessarily K"ahler. It has been conjectured that if a compact complex manifold (M,J) has an SKT metric and a balanced metric both compatible with J, then (M, J) is necessarily K"ahler. We show that the conjecture is true for nilmanifolds.