Nonlinear Dirac operator and quaternionic analysis
Andriy Haydys
TL;DR
This paper explores the properties of the nonlinear Dirac operator and quaternionic analysis, focusing on solutions to the Cauchy-Riemann-Fueter equation and their relation to harmonic spinors in quaternionic geometry.
Contribution
It introduces new insights into the solutions of the Cauchy-Riemann-Fueter equation and links them to harmonic spinors of a generalized nonlinear Dirac operator.
Findings
Solutions for maps from a K3-surface to the cotangent bundle of complex projective space are computed.
A relationship between harmonic spinors and solutions of the Cauchy-Riemann-Fueter equation is established.
Properties of the nonlinear Dirac operator in quaternionic analysis are characterized.
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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