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Bull. Korean Math. Soc. 2019; 56(6): 1551-1567

Online first article August 20, 2019      Printed November 30, 2019

https://doi.org/10.4134/BKMS.b181273

Copyright © The Korean Mathematical Society.

Seiberg-Witten-like equations on the strictly pseudoconvex $CR$-3 manifolds

Serhan Eker

A\u{g}r\i \ \.{I}brah\i m \c{C}e\c{c}en University

Abstract

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In this paper, Seiberg-Witten-like equations are written down on $3$-manifolds. Then, it has been proved that the $L^{2}$-solutions of these equations are trivial on $\mathbb{R}^3$. Finally, a global solution is obtained on the strictly pseudoconvex $CR$-3 manifolds for a given constant negative scalar curvature.

Keywords: Spin and Spin$^c$ geometry, Clifford algebras, spinors, Seiberg-Witten equations

MSC numbers: Primary 53C27, 15A66, 34L40

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