<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Pseudo-Riemannian spinc manifolds were introduced by Ikemakhen in [7]. In the present work we consider pseudo-Riemannian 4-manifolds with neutral signature whose structure groups are SO+(2; 2). We prove that such manifolds have pseudo-Riemannian spinc structure. We construct spinor bundle S and half-spinor bundles S+ and S- on these manifolds. For the first Seiberg-Witten equation we define Dirac operator on these bundles. Due to the neutral metric self-duality of a 2-form is meaningful and it enables us to write down second Seiberg-Witten equation. Lastly we write down the explicit forms of these equations on 4-dimensional at space</p></abstract>

Pseudo-Riemannian spinc manifolds were introduced by Ikemakhen in [7]. In the present work we consider pseudo-Riemannian 4-manifolds with neutral signature whose structure groups are SO+(2; 2). We prove that such manifolds have pseudo-Riemannian spinc structure. We construct spinor bundle S and half-spinor bundles S+ and S- on these manifolds. For the first Seiberg-Witten equation we define Dirac operator on these bundles. Due to the neutral metric self-duality of a 2-form is meaningful and it enables us to write down second Seiberg-Witten equation. Lastly we write down the explicit forms of these equations on 4-dimensional at space

Seiberg-Witten Equations on Pseudo-Riemannian Spin<sup>c</sup> Manifolds With Neutral Signature

Department of Mathematics, Anadolu University, Eskişehir, Turkey

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Seiberg-Witten Equations on Pseudo-Riemannian Spin Manifolds With Neutral Signature

Pseudo-Riemannian spinc manifolds were introduced by Ikemakhen in [7]. In the present work we consider pseudo-Riemannian 4-manifolds with neutral signature...

Seiberg-Witten Equations on Pseudo-Riemannian Spin^c Manifolds With Neutral Signature

Published Online: May 17, 2013

Page range: 73 - 88

DOI: https://doi.org/10.2478/v10309-012-0006-7

Keywords
Neutral metric, Pseudo-Riemannian spinc -structure, Dirac operator, Seiberg-Witten equations

This content is open access.

Seiberg-Witten Equations on Pseudo-Riemannian Spinc Manifolds With Neutral Signature