On a relation between potentials for pluriharmonic maps and para-pluriharmonic maps

TL;DR

This paper explores the connection between pluriharmonic and para-pluriharmonic maps using the loop group method, providing examples and examining implications for CMC-surfaces.

Contribution

It introduces a novel approach to relate pluriharmonic and para-pluriharmonic maps via the loop group method, with practical examples and applications to CMC-surfaces.

Findings

Established a method to interrelate pluriharmonic and para-pluriharmonic maps

Provided explicit examples illustrating the relation

Investigated implications for constant mean curvature surfaces

Abstract

In this paper, we show that one can interrelate pluriharmonic maps with para-pluriharmonic maps by means of the loop group method. As an appendix, we give examples for the interrelation between pluriharmonic maps and para-pluriharmonic maps. Moreover, we investigate the relation among CMC-surfaces by use of such maps.