Riemann slice-domains over quaternions I

Abstract

We construct a counterexample to a well-known extension theorem for slice regular functions, which motivates us to develop a theory of Riemann slice-domains by introducing a new topology on quaternions. By some paths describing axial symmetry in Riemann slice-domains, we rectify the classical extension formula in the theory of slice regular functions and prove a representation formula over slice-domains of regularity. This proof involves an intertwining relation between imaginary units of quaternions and a fixed matrix corresponding to a complex structure.

arXiv comment41 pages

References in corpus (7)

• Slice regular functions on real alternative algebras
• Power series and analyticity over the quaternions
• Twistor transforms of quaternionic functions and orthogonal complex structures
• A new series expansion for slice regular functions
• The Schwarz-Pick lemma for slice regular functions
• Singularities of slice regular functions over real alternative *-algebras
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Cited by in corpus (1)

• Geometric function theory over quaternionic slice domains