Annals of Global Analysis and Geometry

, Volume 53, Issue 4, pp 503–520 | Cite as

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



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.


Moduli space Einstein–Hermitian connection Harmonic mapping Complex projective line Complex hyperquadric Grassmannian manifold 

Mathematics Subject Classification

53C07 58E20 



The first-named author would like to thank the hospitality of Meiji University where part of this work was developed. The work of the first-named author was supported by the Spanish Agency of Scienctific and Technological Research (DGICT) and FEDER project MTM20136961. The work of the second-named author was supported by JSPS KAKENHI Grant Number 17K05230.


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© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Mathematical SciencesUniversity of ValenciaValenciaSpain
  2. 2.Department of MathematicsMeiji UniversityKawasaki-shiJapan

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