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Nonlinear Dirac Operator and Quaternionic Analysis

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Abstract

Properties of the Cauchy–Riemann–Fueter equation for maps between quaternionic manifolds are studied. Spaces of solutions in case of maps from a K3–surface to the cotangent bundle of a complex projective space are computed. A relationship between harmonic spinors of a generalized nonlinear Dirac operator and solutions of the Cauchy–Riemann–Fueter equation are established.

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Authors and Affiliations

  1. Fakultät für mathematik, Universität Bielefeld, Postfach 100131, 33501, Bielefeld, Germany

    Andriy Haydys

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  1. Andriy Haydys
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Correspondence to Andriy Haydys.

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Communicated by G.W. Gibbons

This paper is based upon part of the author’s thesis; he was partially supported by the grant “Gauge theory and exceptional geometry” (Universität Bielefeld) while preparing the final form.

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Haydys, A. Nonlinear Dirac Operator and Quaternionic Analysis. Commun. Math. Phys. 281, 251–261 (2008). https://doi.org/10.1007/s00220-008-0445-1

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  • DOI: https://doi.org/10.1007/s00220-008-0445-1

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