Seiberg-Witten-like equations on the strictly pseudoconvex $CR$-3 manifolds
Bull. Korean Math. Soc. 2019 Vol. 56, No. 6, 1551-1567
https://doi.org/10.4134/BKMS.b181273
Published online August 20, 2019
Printed November 30, 2019
Serhan Eker
A\u{g}r\i \ \.{I}brah\i m \c{C}e\c{c}en University
Abstract : 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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