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Pełne teksty:
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
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
Słowa kluczowe
Tematy
Kategoryzacja MSC:
- 53C10: G -structures
- 32K15: Differentiable functions on analytic spaces, differentiable spaces
- 15A63: Quadratic and bilinear forms, inner products \SeeMainly{}
- 32A30: Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30)
- 30G35: Functions of hypercomplex variables and generalized variables
- 15A66: Clifford algebras, spinors
- 53C40: Global submanifolds
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
autor
- Institute of Mathematics, Polish Academy of Sciences, Łódź Branch, Narutowicza 56, PL-90-136 Łódź, Poland
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Języki publikacji
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Uwagi
1991 Mathematics Subject Classification: 15A63, 15A66, 30G35, 32A30, 32K15, 53C10-53C40.
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