Vanishing theorems and string backgrounds
Vanishing theorems and string backgrounds
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DOI：
10.1088/0264-9381/18/6/309
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发表时间：
2000-10
影响因子：
3.5
通讯作者：
Stefan Ivanov;G. Papadopoulos
中科院分区：
文献类型：
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作者：
Stefan Ivanov;G. Papadopoulos
对于Bismut连接具有包含在SU(n)中的（限制）完整的紧密密流形的上同调群，给出了各种消失定理，并对所有这些四维的紧密密流形进行了分类。从而在非kahler型第一Chern类消失的紧厄米流形上给出了这种结构存在的必要条件。然后，我们将我们的结果应用于弦方程的解，并证明这些解承认各种上同调限制，例如，在某些自然假设下，多属消失。我们还发现，在某些假设下，弦方程等价于某个向量相对于Bismut连接平行的条件。
We show various vanishing theorems for the cohomology groups of compact Hermitian manifolds for which the Bismut connection has a (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 compact Hermitian manifolds with vanishing first Chern class of non-Kahler type. Then we apply our results to solutions of the string equations and show that such solutions admit various cohomological restrictions such as, 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.