Cauchy-Riemann equations and Jacobians of quaternion polynomials

2016/09/14 by Takis Sakkalis, Sakkalis, Takis, Sofia Douka +1
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Advanced Differential Geometry Research #Advanced Differential Equations and Dynamical Systems

paper · pdf · doi:10.48550/arxiv.1609.04193

Abstract

A map f from the quaternion skew field H to itself, can also be thought as a transformation f:R⁴ → R⁴. In this manuscript, the Jacobian J(f) of f is computed, in the case where f is a quaternion polynomial. As a consequence, the Cauchy-Riemman equations for f are derived. It is also shown that the Jacobian determinant of f is non negative over H. The above commensurates well with the theory of analytic functions of one complex variable.

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