Calibrations and Manifolds with Special Holonomy
The purpose of this paper is to introduce Harvey–Lawson manifolds and review the construction of certain “mirror dual” Calabi–Yau submanifolds inside a G 2 manifold. More specifically, given a Harvey–Lawson manifold HL, we explain how to assign a pair of tangent bundle valued 2 and 3-forms to a G 2 manifold \((M,HL,\varphi,\varLambda )\), with the calibration 3-form \(\varphi\) and an oriented 2-plane field Λ. As in  these forms can then be used to define different complex and symplectic structures on certain 6-dimensional subbundles of T(M). When these bundles are integrated they give mirror CY manifolds (related through HL manifolds).
KeywordsCross Product Symplectic Structure Tubular Neighborhood Bundle Versus Unit Section
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