A gauge theoretic aspects of parabolic bundles over Klein surfaces

In this article, we study the gauge theoretic aspects of real and quaternionic parabolic bundles over a real curve (X,?X), where X is a compact Riemann surface and {\sigma}X is an anti-holomorphic involution. For a fixed real or quaternionic structure on a smooth parabolic bundle, we examine the orbits space of real or quaternionic connection under the appropriate gauge group. The corresponding gauge-theoretic quotients sit inside the real points of the moduli of holomorphic parabolic bundles having a fixed parabolic type on a compact Riemann surface X.