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Turkish Journal of Mathematics

DOI

10.3906/mat-1303-34

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^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.

First Page

812

Last Page

818

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Mathematics Commons

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