Nonlinear Dirac operator and quaternionic analysis. (English) Zbl 1230.30034

Summary: 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.


30G35 Functions of hypercomplex variables and generalized variables
53C26 Hyper-Kähler and quaternionic Kähler geometry, “special” geometry
35Q40 PDEs in connection with quantum mechanics
58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
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