Seiberg-Witten Like Equations on Pseudo-Riemannian Spin.. Manifolds with G(2(2))* Structure

Abstract

We consider 7-dimensional pseudo-Riemannian spin(c) manifolds with structure group G(2(2))*. On such manifolds, the space of 2-forms splits orthogonally into components Lambda M-2 = Lambda(2)(7) circle plus Lambda(2)(14). We define self-duality of a 2-form by considering the part Lambda(2)(7) 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 R-4,R-3 and give some solutions.