消灭定理与弦背景
Vanishing Theorems and String Backgrounds
摘要：
本文给出了紧厄米流形的上同调群的各种消灭定理，并对所有四维厄米流形进行了分类.这样，我们就提供了埃尔米特流形上这种结构存在的必要条件。然后，我们将我们的结果的解决方案的字符串方程，并表明，这样的解决方案承认各种上同调的限制，例如，在某些自然的假设下，plurigenes消失。我们还发现，在某些假设下，弦方程等价于某个向量平行于Bismut联络的条件。
英文摘要：
We show various vanishing theorems for the cohomology groups of compact hermitian manifolds for which the Bismut connection has (restricted) holonomy contained in SU(n) and classify all such manifolds of dimension four. In this way we provide necessary conditions for the existence of such structures on hermitian manifolds. Then we apply our results to solutions of the string equations and show that such solutions admit various cohomological restrictions like for example that under certain natural assumptions the plurigenera vanish. We also find that under some assumptions the string equations are equivalent to the condition that a certain vector is parallel with respect to the Bismut connection.
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