Abstract
This work presents an extension, called coordinate slice extension, of the union of a finite number of axially symmetric s domains according to the fiber bundle theory and a kind of slice regular functions are defined on this coordinate slice extension.
Similar content being viewed by others
Data Availibility
Not applicable.
Code availability
Not Applicable.
References
Bernstein, H.J., Philips, A.: Fiber Bundles and Quantum Theory. Sci. Am. 245(1), 122–137 (1981)
Bleecker, D.: Gauge theory and variational principles. Dover Books on physics Dover Books on mathemtics, Courier Corporation (2005)
Bredon, G.E.: Topology and Geometry. Springer Verlang (1913)
Cohen, R.L.: The topology of fiber bundles. Stanford University (1998)
Colombo, F., Sabadini, I.: A structure formula for slice monogenic functions and some of its consequences, Hypercomplex Analysis, Trends in Mathematics, Birkhäuser, 101–114 (2009)
Colombo, F., González-Cervantes, J.O., Sabadini, I.: The C-property for slice regular functions and applications to the Bergman space. Compl. Var. Ell. Equa. 58, 1355–1372 (2013)
Colombo, F., Sabadini, I., Struppa, D.C.: Noncommutative Functional Calculus. Theory and Applications of Slice Hyperholomorphic Functions, Birkhauser, Basel, 289 (2011)
Colombo, F., Sabadini, I., Struppa, D.C.: Algebraic Properties of the Module of Slice Regular Functions in Several Quaternionic Variables. Indiana Univ. Math. J. 61(4), 1581–1602 (2012)
Colombo, F., Gentili, G., Sabadini, I., Struppa, D.C.: Extension results for slice regular functions of a quaternionic variable. Adv. Math. 222, 1793–1808 (2009)
Colombo, F., Sabadini, I., Struppa, D. C.: Entire slice regular functions. Springer Briefs in Mathematics, Springer, (2016)
Dou, X., Ren, G., Sabadini, I., Wang, X.: Slice quaternionic analysis in two variables. Complex Var. Elliptic Equ. 67(8), 1907–1930 (2022)
Dou, X., Ren, G., Sabadini, I.: A representation formula for slice regular functions over slice-cones in several variables. Annali di Matematica (1923). https://doi.org/10.1007/s10231-023-01325-y
Ghiloni, R., Perotti, A.: Slice regular functions in several variables. Math. Z. 302, 295–351 (2022). https://doi.org/10.1007/s00209-022-03066-9
González-Cervantes, J. O.: A fiber bundle over the quaternionic slice regular functions. Advances in Applied Clifford Algebras (IF1.072), Pub Date : 2021-06-21, https://doi.org/10.1007/s00006-021-01158-z
González-Cervantes, J. O.: Quaternionic slice regular functions associated with some sphere bundles. Complex Variables and Elliptic Equations, (2021) 1–12. https://doi.org/10.1080/17476933.2021.1971658
González-Cervantes, J. O.: On fiber bundles and quaternionic slice regular functions. Complex Analysis and Operator Theory, (2022)
González-Cervantes, J.O., Sabadini, I.: On some splitting properties of slice regular functions. Compl. Var. Ell. Equa. 62, 1393–1409 (2017)
Gentili, G., Stoppato, C., Struppa, D.C.: Regular functions of a quaternionic variable. Springer Monographs in Mathematics. Springer, Heidelberg (2013)
Grauert, H., Peternell, Th., Remmert, R.: Several Several Complex Variables VII: Sheaf-Theoretical Methods in Complex Analysis, Encyclopaedia of mathematical science, Springer Verlag, 74 (1991)
Hatcher, A.: Algebraic-Topology. Cambridge University Press, Cambridge (2002)
Heidrich, R., Jank, G.: On iteration of quaternionic Möbius transformation. Compl. Var. Theory Appls. 29, 313–318 (1996)
Husemoller, D.: Fibre Bundles, 3rd edn. Springer, New York (1993)
Krantz, S.: Function theory of several complex variables, 2nd edn. American Mathematical Society (2001)
Steenrod, N.: The topology of fibre bundles. Princeton University Press, Princeton NJ (1951)
Walschap, G.: Metric Structures in Differential Geometry. Springer (2004)
Weatherall, J.O.: Fiber bundles, Yang-Mills theory, and general relativity. Synthese 193, 2389–2425 (2016)
Funding
Instituto Politécnico Nacional (grant number SIP20232103) and CONACYT.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The author declare that he has no conflict of interest regarding the publication of this paper.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This work was partial supported by CONACYT.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
González-Cervantes, J.O. An Extension of Slice Regular Functions in Terms of Fiber Bundle Theory. Adv. Appl. Clifford Algebras 34, 5 (2024). https://doi.org/10.1007/s00006-023-01309-4
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00006-023-01309-4