Polynomial harmonic morphisms between Euclidean spheres
Authors:
James Eells and Paul Yiu
Journal:
Proc. Amer. Math. Soc. 123 (1995), 29212925
MSC:
Primary 58E20; Secondary 55R25
MathSciNet review:
1273489
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Abstract: A characterization is given of the harmonic morphisms between euclidean spheres whose component functions are harmonic homogeneous polynomials of the same degree, and also of polynomial harmonic morphisms between euclidean spaces which map spheres into spheres. These turn out to be isometric to the classical Hopf fibrations.
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 [B2]
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 P. Baird and A. Ratto, Conservation laws, equivariant harmonic maps and harmonic morphisms, Proc. London Math. Soc. (3) 64 (1992), 197224. MR 1132860 (93a:58045)
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 P. Baird and J.C. Wood, Bernstein theorems for harmonic morphisms from and , Math. Ann. 280 (1988), 579603. MR 939920 (90e:58027)
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 W. Browder, Higher torsion in Hspaces, Trans. Amer. Math. Soc. 108 (1965), 353375. MR 0155326 (27:5260)
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 J. Eells and N. Kuiper, An invariant for certain smooth manifolds, Ann. Mat. Pura Appl. 60 (1963), 93110. MR 0156356 (27:6280)
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 J. Eells and L. Lemaire, A report on harmonic maps, Bull. London Math. Soc. 10 (1978), 168. MR 495450 (82b:58033)
 [EL2]
 , Topics in harmonic maps, CBMS Regional Conf. Ser. in Math., vol. 50, Amer. Math. Soc., Providence, RI, 1983.
 [EL3]
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 [F]
 B. Fuglede, Harmonic morphisms between Riemannian manifolds, Ann. Inst. Fourier (Grenoble) 28 (1978), 107144. MR 499588 (80h:58023)
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 G. Gigante, A note on harmonic morphisms, preprint, 1983.
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 M. Koecher and R. Remmert, "Composition algebras. Hurwitz's theoremvector product algebras", Chapter 10 in H.D. Ebbinghaus et al., Numbers, Graduate Texts in Math., vol. 123, SpringerVerlag, Berlin, 1990, pp. 265280. MR 1066206 (91h:00005)
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 [Y]
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199512734894
PII:
S 00029939(1995)12734894
Keywords:
Harmonic morphisms,
Hopf fibrations,
orthogonal multiplications,
polynomial maps between spheres
Article copyright:
© Copyright 1995 American Mathematical Society
