On Fiber Bundles and Quaternionic Slice Regular Functions

Abstract

The papers (González-Cervantes in Adv Appl Clifford Algebras 31:55, 2021; González-Cervantes Complex Variables and Elliptic Equations 2021) are the first works to apply the theory of fiber bundles in the study of the quaternionic slice regular functions. The main goal of the present work is to extend the results given in González-Cervantes (2021), where the quaternionic right linear space of quaternionic slice regular functions was presented as the base space of a fiber bundle. When the quaternionic right linear space of quaternionic slice regular functions is associated to certain domains then this paper shows that the elements of total space, given in González-Cervantes (2021), are defined from a pair of harmonic functions and a pair of orthogonal vectors. Simplifying the computations presented in González-Cervantes (2021), where each element of the total space is formed by two pair of conjugate harmonic functions and a pair of orthogonal unit vectors. This work also gives some interpretations of the behavior of the zero sets of some quaternionic slice regular polynomials in terms of the theory of fiber bundles.