Pluriharmonic Morphisms

TL;DR

This paper investigates pluriharmonic morphisms, exploring their relationships with various types of maps and characterizing them between Hermitian manifolds, especially when the target is Kähler, to deepen understanding of their structure.

Contribution

It provides a detailed analysis of pluriharmonic morphisms, including their inter-relationships and a characterization between Hermitian manifolds, with a focus on Kähler targets.

Findings

Characterization of pluriharmonic morphisms between Hermitian manifolds.

Analysis of relationships between (1,1)-geodesic, pluriharmonic, and holomorphic maps.

Special understanding of pluriharmonic morphisms when the target is Kähler.

Abstract

Pluriharmonic maps form an important class of harmonic maps which includes holomorphic maps. We study their morphisms, in particular the inter-relationships between $(1,1)$-geodesic, pluriharmonic and $\pm$holomorphic maps. Then we characterise pluriharmonic morphisms between Hermitian manifolds. We make a special study of the situation where the target is K{\"a}hler, pluriharmonic morphisms being particularly well understood for this case.