Mirror Duality via G_2 and Spin(7) Manifolds
Mirror Duality via G_2 and Spin(7) Manifolds
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通过 G_2 和 Spin(7) 流形镜像对偶性
DOI：
10.1007/978-0-8176-4831-2_1
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
S. Salur
中科院分区：
文献类型：
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作者：
S. Akbulut;S. Salur
本章的主要目的是给出aG2流形内的某些“镜像对偶”Calabi-Yau子流形的构造。更具体地说，我们解释了如何给一个G2流形(M， φ，Λ)赋值为2-和3-形式的参数化切丛，该流形具有校准的3-形式φ和定向的2-平面场Λ。然后，这些形式可以用来定义FT(M)的某些6维子丛上不同的复结构和辛结构。当这些丛被积分时，它们得到镜像CY流形。用类似的方法，人们可以在ASpin(7)流形(N8，Ψ)内定义镜像对G2流形。在N_8取有向3-平面场的情况下，通过迭代得到N中的Calabi-Yau子流形对，其复结构和辛结构通过环境G_2(或Spin(7))流形的校准形式相互决定。
The main purpose of this chapter is to give a construction of certain “mirror dual” Calabi–Yau submanifolds inside of aG2manifold. More specifically, we explain how to assign to aG2manifold (M, φ,Λ), with the calibration 3-form φ and an oriented 2-plane fieldΛ, a pair of parametrized tangent bundle valued 2- and 3-forms ofM. These forms can then be used to define different complex and symplectic structures on certain 6-dimensional subbundles ofT(M). When these bundles are integrated they give mirror CY manifolds. In a similar way, one can define mirror dualG2manifolds inside of aSpin(7) manifold (N8,Ψ). In caseN8admits an oriented 3-plane field, by iterating this process we obtain Calabi–Yau submanifold pairs inNwhose complex and symplectic structures determine each other via the calibration form of the ambientG2(orSpin(7)) manifold.