Moduli of Einstein–Hermitian harmonic mappings of the projective line into quadrics

Abstract

The present article studies the class of Einstein–Hermitian harmonic maps of constant Kähler 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 are examined. Finally, certain classical results concerning embeddings of two-dimensional spheres into spheres are rephrased and derived in our formalism.