Seiberg-Witten-Like Equations Without Self-Duality on Odd Dimensional Manifolds

Abstract

In this paper, Seiberg-Witten-like equations without self-duality are defined on any smooth 2n+1-dimensional Spin^c manifolds. Then, a non-trivial solution is given on the strictly-Pseudoconvex CR-5 manifolds endowed with a canonical Spin^c- structure by using Dirac operator associated with the generalized Tanaka-Webster connection. Finally, some bounds are given to them on the 5-dimensional Riemannian manifolds.