On quaternionic analysis and its modifications (Q1880510)

Quaternionic analysis is a function theory related to the Euclidean metric in \(\mathbb R^4\), in the same way Clifford analysis is related to the Euclidean metric in an arbitrary \(\mathbb R^n\) . A few years ago the first-named author introduced a modification of the above theories based on hyperbolic metric. There exists also a theory developed by G. Laville and I. Ramodanoff which is a unification, in a sense, of both. What is being done in the paper, is a comparison of three theories with each other.