# Moduli of Einstein-Hermitian harmonic mappings of the projective line into quadrics

## TL;DR

This paper investigates the moduli spaces of Einstein-Hermitian harmonic maps from the projective line into quadrics, revealing their structure, independence from certain constants, and connections to classical sphere embeddings.

## Contribution

It provides a detailed description of the moduli spaces of these harmonic maps using vector bundles and representation theory, including rigidity and classical embedding results.

## Key findings

- Moduli space dimension is independent of the Einstein-Hermitian constant.
- Rigidity of real standard and totally real maps is analyzed.
- Classical sphere embedding results are reinterpreted within this framework.

## Abstract

The present article studies the class of Einstein-Hermitian harmonic maps of constant Kaehler angle from the projective line into quadrics. We provide a description of their moduli spaces up to image, and gauge-equivalence using the language of vector bundles and representation theory. It is shown that the dimension of the moduli spaces is independent of the Einstein-Hermitian constant, and rigidity of the associated real standard, and totally real maps is examined. Finally, certain classical results concerning embeddings of two-dimensional spheres into spheres are rephrased and derived in our formalism.