Form-Type Calabi-Yau Equations
Form-Type Calabi-Yau Equations
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DOI：
10.4310/mrl.2010.v17.n5.a7
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发表时间：
2009-08
期刊：
影响因子：
--
通讯作者：
Jixiang Fu;Zhizhang Wang;Damin Wu
中科院分区：
文献类型：
--
作者：
Jixiang Fu;Zhizhang Wang;Damin Wu
从超弦理论的数学方面出发，我们引入了一个新的方程的平衡，厄米流形，零第一陈类。解此方程，在每个Bott-Chern上同调类中，将得到一个Hermitian Ricci平坦的平衡度量.这可以看作是经典Calabi-Yau方程的微分形式水平的推广。在复环面上建立了方程的存在性和唯一性，并证明了在一般K\“ahler流形上方程的唯一性和开性.
Motivated from mathematical aspects of the superstring theory, we introduce a new equation on a balanced, hermitian manifold, with zero first Chern class. Solving the equation, one will obtain, in each Bott--Chern cohomology class, a balanced metric which is hermitian Ricci--flat. This can be viewed as a differential form level generalization of the classical Calabi--Yau equation. We establish the existence and uniqueness of the equation on complex tori, and prove certain uniqueness and openness on a general K\"ahler manifold.