In this paper, we write Seiberg--Witten-like equations on contact metric manifolds of dimension 5. Since any contact metric manifold has a Spin^c-structure, we use the generalized Tanaka--Webster connection on a Spin^c 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.
Seiberg--Witten equations, spinor, Dirac operator, contact metric manifold, self-duality
DEĞİRMENCİ, NEDİM and BULUT, ŞENAY
"Seiberg--Witten-like equations on 5-dimensional contact metric manifolds,"
Turkish Journal of Mathematics: Vol. 38:
5, Article 2.
Available at: https://journals.tubitak.gov.tr/math/vol38/iss5/2