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

Abstract

In this paper, we write Seiberg–Witten-like equations on contact metric manifolds of dimension 5. Since any contact metric manifold has a Spinc -structure, we use the generalized Tanaka–Webster connection on a Spinc 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

In this paper, we write Seiberg–Witten-like equations on contact metric manifolds of dimension 5. Since any contact metric manifold has a Spinc -structure, we use the generalized Tanaka–Webster connection on a Spinc 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