Mirror Duality via G_2 and Spin(7) Manifolds
| dc.creator | Akbulut, Selman | |
| dc.creator | Salur, Sema | |
| dc.date | 2006-05-10 | |
| dc.date | 2007-06-14 | |
| dc.date.accessioned | 2026-07-07T08:09:56Z | |
| dc.date.available | 2026-07-07T08:09:56Z | |
| dc.description | The main purpose of this paper is to give a mathematical definition of ``mirror symmetry'' for Calabi-Yau and G_2 manifolds. More specifically, we explain how to assign a G_2 manifold (M,ϕ,Λ), with the calibration 3-form ϕand an oriented 2-plane field Λ, a pair of parametrized tangent bundle valued 2 and 3-forms of M. These forms can then be used to define various different complex and symplectic structures on certain 6-dimensional subbundles of T(M). When these bundles are integrated they give mirror CY manifolds. In a similar way, one can define mirror dual G_2 manifolds inside of a Spin(7) manifold (N^8, Ψ). In case N^8 admits an oriented 3-plane field, by iterating this process we obtain Calabi-Yau submanifold pairs in N whose complex and symplectic structures determine each other via the calibration form of the ambient G_2 (or Spin(7)) manifold. | |
| dc.description | Revised version, remarks added, 20 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/math/0605277 | |
| dc.identifier | http://arxiv.org/abs/math/0605277 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131695 | |
| dc.subject | Differential Geometry | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Geometric Topology | |
| dc.title | Mirror Duality via G_2 and Spin(7) Manifolds | |
| dc.type | text |