Harvey Lawson Manifolds and Dualities
Differential Geometry
2015-01-21 v1
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, \Lambda), with the calibration 3-form \varphi and an oriented 2-plane field \Lambda. These forms can then be used to define different complex and symplectic structures on certain 6-dimensional sub bundles of T(M). When these bundles are integrated they give mirror CY manifolds (related thru HL manifolds).
Keywords
Cite
@article{arxiv.1501.04783,
title = {Harvey Lawson Manifolds and Dualities},
author = {Selman Akbulut and Sema Salur},
journal= {arXiv preprint arXiv:1501.04783},
year = {2015}
}
Comments
9 pages, LaTex. arXiv admin note: text overlap with arXiv:math/0605277