Seiberg-Witten-like equations on 5-dimensional contact metric manifolds

DEĞİRMENCİ N., BULUT Ş.

TURKISH JOURNAL OF MATHEMATICS, vol.38, no.5, pp.812-818, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 5
  • Publication Date: 2014
  • Doi Number: 10.3906/mat-1303-34
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.812-818
  • Keywords: Seiberg-Witten equations, spinor, Dirac operator, contact metric manifold, self-duality, MONOPOLE EQUATIONS, FIELDS
  • Anadolu University Affiliated: Yes

Abstract

In this paper, we write Seiberg-Witten-like equations on contact metric manifolds of dimension 5. Since any contact metric manifold has a Spin(e)-structure, we use the generalized Tanaka-Webster connection on a Spin(e) spinor bundle of a contact metric manifold to define the Dirac-type operators and write the Dirac equation. The self-duality of 2-forms needed for the curvature equation is defined by using the contact structure. These equations admit a nontrivial solution on 5-dimensional strictly pseudoconvex CR manifolds whose contact distribution has a negative constant scalar curvature.