On Fueter-Hurwitz regular mappings

Królikowski Wiesław

GDML_Books, (1996), p.

Abstract

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.......................................................................................................88

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Zbl 0864.30038

EUDML-ID : urn:eudml:doc:270072