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On Fueter-Hurwitz regular mappings

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Królikowski W.

Instytut Matematyczny Polskiej Akademii Nauk

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

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1 Królikowski W.

1 1996

Wyniki wyszukiwania

On Fueter-Hurwitz regular mappings