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

DEĞİRMENCİ N., BULUT Ş.

Balkan Journal of Geometry and its Applications, vol.20, no.2, pp.23-31, 2015 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 2
  • Publication Date: 2015
  • Journal Name: Balkan Journal of Geometry and its Applications
  • Journal Indexes: Scopus
  • Page Numbers: pp.23-31
  • Keywords: Dirac operator, Seiberg-Witten equations, Spinor, SU(3)-manifold
  • Anadolu University Affiliated: Yes

Abstract

© Balkan Society of Geometers, Geometry Balkan Press 2015.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 Λ2(M) = Λ12 (M) ⊕ Λ62 (M) ⊕ Λ82 (M) [1]. We consider the part Λ12 (M) ⊕ Λ62 (M) as the bundle of self-dual 2-forms. Lastly, we give a global solution for these equations.