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Demonstratio Mathematica

Editor-in-Chief: Vetro, Calogero


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CiteScore 2017: 0.28
SCImago Journal Rank (SJR) 2017: 0.231
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ICV 2017: 121.78



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2391-4661
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Volume 47, Issue 4

Issues

New Geometric Interpretation of Quaternionic Fueter Functions

Wiesław Królikowski
Published Online: 2014-12-11 | DOI: https://doi.org/10.2478/dema-2014-0062

Abstract

A correspondence between quaternionic regular functions in the sense of Fueter and fundamental 2-forms on a 4-dimensional almost Kähler manifold is shown.

Keywords: and phrases fundamental 2-form; almost Kähler manifold (complex analysis); Fueter regular function (quaternionic analysis)

References

  • [1] D. E. Blair, Nonexistence of 4-dimensional almost Kähler manifolds of constant curvature, Proceedings of the American Mathematical Society, Vol. 110, No. 4, 1990.Google Scholar

  • [2] W. Królikowski, On Fueter-Hurwitz regular mappings, Dissertationes Math. 353 (1996).Google Scholar

  • [3] W. Królikowski, On 4-dimensional locally conformally flat almost Kähler manifolds, Arch. Math. (Brno) 42(3) (2006), 215-223.Google Scholar

  • [4] W. Królikowski, Some problems of quaternionic analysis, Częstochowa University of Technology, Częstochowa, 2012.Google Scholar

  • [5] S. Kobayashi, K. Nomizu, Foundations of Differentaial Geometry, Vol. I - II, Interscience, 1963.Web of ScienceGoogle Scholar

  • [6] R. Fueter, Die Funktionentheorie der Differentialgleichungen Δu = 0 und ΔΔu = 0 mit vier reellen Variablen, Comment. Math. Helv. 7 (1935), 307-330.Google Scholar

  • [7] A. Sudbery, Quaternionic analysis, Math. Proc. Cambridge Philos. Soc. 85 (1979), 199-225.Google Scholar

About the article

Received: 2013-09-02

Revised: 2014-05-05

Published Online: 2014-12-11

Published in Print: 2014-12-01


Citation Information: Demonstratio Mathematica, Volume 47, Issue 4, Pages 776–783, ISSN (Online) 2391-4661, ISSN (Print) 0420-1213, DOI: https://doi.org/10.2478/dema-2014-0062.

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© by Wiesław Królikowski. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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