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On Fueter-Hurwitz regular mappings

Seria
Rozprawy Matematyczne tom/nr w serii: 353 wydano: 1996
Zawartość
Warianty tytułu
Abstrakty
CONTENTS
Introduction........................................................................................................6
I. 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.................................................................24
II. &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........................................................58
III. &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.......................................................................................................88
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 353
Liczba stron
91
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCLIII
Daty
wydano
1996
otrzymano
1994-03-02
poprawiono
1995-03-17
Twórcy
  • Institute of Mathematics, Polish Academy of Sciences, Łódź Branch, Narutowicza 56, PL-90-136 Łódź, Poland
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Języki publikacji
EN
Uwagi
1991 Mathematics Subject Classification: 15A63, 15A66, 30G35, 32A30, 32K15, 53C10-53C40.
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0012-3862
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