Calibrations and Manifolds with Special Holonomy

  • Selman Akbulut
  • Sema Salur
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 106)


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 [3] 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).


Cross Product Symplectic Structure Tubular Neighborhood Bundle Versus Unit Section 
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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA
  2. 2.Department of MathematicsUniversity of RochesterRochesterUSA

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