A general Schwarz Lemma for almost-Hermitian manifolds
A general Schwarz Lemma for almost-Hermitian manifolds
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DOI：
10.4310/cag.2007.v15.n5.a6
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发表时间：
2007-07
期刊：
影响因子：
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通讯作者：
Valentino Tosatti
中科院分区：
文献类型：
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作者：
Valentino Tosatti
我们证明了一个版本的丘的施瓦茨引理一般几乎复杂的流形配备厄米度量。这需要对拉普拉斯比较定理的这种设置进行扩展。作为一个应用，我们证明了两个几乎复流形的乘积不允许任何完全的厄米特度量，其对分曲率在两个负常数之间有界，满足一些附加的温和假设。
We prove a version of Yau's Schwarz Lemma for general almost-complex manifolds equipped with Hermitian metrics. This requires an extension to this setting of the Laplacian comparison theorem. As an application we show that the product of two almost-complex manifolds does not admit any complete Hermitian metric with bisectional curvature bounded between two negative constants that satisfies some additional mild assumptions.