On Fueter-Hurwitz regular mappings
Królikowski Wiesław
- Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1996
CONTENTSIntroduction........................................................................................................6I. Quaternionic regular and biregular functions in the sense of Fueter..............9 1. Introduction................................................................................................9 2. Fueter derivative and regular functions.....................................................10 3. Quaternionic partial derivatives.................................................................12 4. Functions with holomorphic slices.............................................................14 5. Non-regularity of simple quaternionic power series....................................17 6. Biregular mappings...................................................................................20 7. Leibniz rule for the Fueter operator...........................................................22 8. Regular functions on manifolds.................................................................24II. &Fueter regular functions and harmonicity.....................................................25 1. Introduction...............................................................................................25 2. Quaternionic manifolds-foundations..........................................................26 3. Energies of mappings...............................................................................30 4. Lichnerowicz-type homotopy invariant-quaternionic case.........................33 5. Lichnerowicz-type homotopy invariant for G-structures............................39 a) General situation...................................................................................39 b) Special cases: holonomy groups G₂ and Spin(7)....................................41 c) Generalization of the Lichnerowicz invariant in the complex case............43 6. Stress-energy tensor and harmonic maps.................................................45 Application to the 4-dimensional torus........................................................58III. &Fueter-Hurwitz regular maps and Hurwitz pairs..i.......................................60 1. Introduction................................................................................................60 2. Hurwitz pairs-basic information...................................................................62 3. Fueter-Hurwitz equation..............................................................................64 4. Special polynomial solutions of the Fueter-Hurwitz equation........................65 5. Fourier representation of Fueter-Hurwitz regular mappings.........................68 6. Integral representation of Fueter-Hurwitz regular mappings.........................69 7. Anisotropic complex structure on the pseudo-Euclidean Hurwitz pairs..........75 8. Pairs of Clifford algebras of Hurwitz type.......................................................85 Acknowledgements...........................................................................................88 References.......................................................................................................881991 Mathematics Subject Classification: 15A63, 15A66, 30G35, 32A30, 32K15, 53C10-53C40.
Królikowski Wiesław. On Fueter-Hurwitz regular mappings. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1996. <http://eudml.org/doc/270072>.
@book{KrólikowskiWiesław1996,
author = {Królikowski Wiesław},
keywords = {generalized Cauchy-Riemann equations; Fueter-Hurwitz equation; hypercomplex regular functions; quaternionic analysis; quaternionic manifolds; Fueter theory; Hurwitz pairs},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {On Fueter-Hurwitz regular mappings},
url = {http://eudml.org/doc/270072},
year = {1996},
}
TY - BOOK
AU - Królikowski Wiesław
TI - On Fueter-Hurwitz regular mappings
PY - 1996
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
LA - eng
KW - generalized Cauchy-Riemann equations; Fueter-Hurwitz equation; hypercomplex regular functions; quaternionic analysis; quaternionic manifolds; Fueter theory; Hurwitz pairs
UR - http://eudml.org/doc/270072
ER -
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