Seiberg-Witten Like Monopole Equations on <em>R</em><sup>5</sup>

Abstract

Seiberg-Witten monopole equations were defined on 4-dimensional Riemannian manifolds in 1994 by E. Witten (see [2]). These are a couple of non-linear partial differential equations on a 4-dimensional Riemannian manifold and give differential topological invariants for the underlying 4-manifold (see [3]). In recent years some generalizations of Seiberg-Witten equations to higher dimensionalmanifolds are studied by various authors (see [4–7]). The purpose of this article is to write down similar equations on R5.