Seiberg-Witten-like equations on 6-dimensional SU(3)-manifolds

Abstract

It is known that Seiberg-Witten monopole equations are important for the investigations of smooth 4-manifolds. In this study we write the similar equations for 6-dimensional manifold M with structure group SU(3). For Dirac equation we use the associated Spinc-structure to the SU(3)-structure. For the curvature equation we make use of the decomposition ?2(M) = ?1 2 (M) ? ?6 2 (M) ? ?8 2 (M) [1]. We consider the part ?1 2 (M) ? ?6 2 (M) as the bundle of self-dual 2-forms. Lastly, we give a global solution for these equations