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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)

Abstract

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).

Keywords

Cross Product Symplectic Structure Tubular Neighborhood Bundle Versus Unit Section 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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