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Advances in Mathematical Physics
Volume 2016, Article ID 2173214, 7 pages
http://dx.doi.org/10.1155/2016/2173214
Research Article

Seiberg-Witten Like Equations on Pseudo-Riemannian Manifolds with Structure

Department of Mathematics, Anadolu University, Eskisehir, Turkey

Received 26 August 2015; Accepted 28 September 2015

Academic Editor: Dimitrios Tsimpis

Copyright © 2016 Nülifer Özdemir and Nedim Deǧirmenci. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider 7-dimensional pseudo-Riemannian manifolds with structure group . On such manifolds, the space of 2-forms splits orthogonally into components . We define self-duality of a 2-form by considering the part as the bundle of self-dual 2-forms. We express the spinor bundle and the Dirac operator and write down Seiberg-Witten like equations on such manifolds. Finally we get explicit forms of these equations on and give some solutions.