Existence and non-existence results for harmonic maps between spheres

Valter Pettinati; Andrea Ratto

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1990)

  • Volume: 17, Issue: 2, page 273-282
  • ISSN: 0391-173X

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Pettinati, Valter, and Ratto, Andrea. "Existence and non-existence results for harmonic maps between spheres." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 17.2 (1990): 273-282. <http://eudml.org/doc/84073>.

@article{Pettinati1990,
author = {Pettinati, Valter, Ratto, Andrea},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {harmonic map; equivariant map},
language = {eng},
number = {2},
pages = {273-282},
publisher = {Scuola normale superiore},
title = {Existence and non-existence results for harmonic maps between spheres},
url = {http://eudml.org/doc/84073},
volume = {17},
year = {1990},
}

TY - JOUR
AU - Pettinati, Valter
AU - Ratto, Andrea
TI - Existence and non-existence results for harmonic maps between spheres
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1990
PB - Scuola normale superiore
VL - 17
IS - 2
SP - 273
EP - 282
LA - eng
KW - harmonic map; equivariant map
UR - http://eudml.org/doc/84073
ER -

References

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  1. [1] P. Baird, Harmonic maps with symmetries, harmonic morphisms, and deformation of metrics, Research Notes in Math, Pitman (1983). Zbl0515.58010
  2. [2] M. Berger, et. al.: Le Spectre d'une Variété Riemannienne, Springer Lecture Notes 194, (1971). Zbl0223.53034
  3. [3] E. Coddington - N. Levinson, Theory of ordinary differential equations, Mc Graw - Hill, (1955). Zbl0064.33002MR69338
  4. [4] W.Y. Ding, Symmetric harmonic maps between spheres, preprint Academia Sinica, (1988). MR962492
  5. [5] M. Do Carmo - N.R. Wallach, Minimal Immersions of Spheres into Spheres, Annals of Mathematics93, (1971), 43-62. Zbl0218.53069MR278318
  6. [6] J. Eells - L. Lemaire, A report on harmonic maps, Bull. London Math. Soc.10, (1978), 1-68. Zbl0401.58003MR495450
  7. [7] J. Eells - L. Lemaire, Examples of harmonic maps from disks to hemispheres, Math. Z185, (1984), 517-519. Zbl0527.58012MR733771
  8. [8] J. Eells - J.C. Polking, Removable singularities of harmonic maps, Indiana U. Math. J.33, (1984), 859-871. Zbl0559.58011MR763946
  9. [9] J. Eells - J.H. Sampson, Harmonic mappings of Riemannian Manifolds, Amer. J. Math.86, (1964), 109-160. Zbl0122.40102MR164306
  10. [10] A. Ratto, Construction d'applications harmoniques de spheres éuclidiennes, C.R. Acad. Sc. Paris, 304, (1987), 186-187. Zbl0612.58014MR880922
  11. [11] A. Ratto, Harmonic maps from deformed spheres to spheres, Amer. J. Math., 111, (1989), 225-238. Zbl0685.58014
  12. [12] A. Ratto, Harmonic maps of spheres and equivariant theory, Ph.D. Thesis, Warwick University, (1987). Zbl0612.58014
  13. [ 13] A. Ratto, Harmonic maps of spheres and the Hopf construction, Topology, to appear. Zbl0692.55010MR1014467
  14. [14] R.T. Smith, Harmonic mappings of spheres, Amer. J. Math.97, (1975), 364-395. Zbl0321.57020MR391127
  15. [15] R.T. Smith, Harmonic mappings of spheres, Ph.D. Thesis, Warwick University, (1972). Zbl0279.53055
  16. [16] R.T. Smith, Harmonic mappings of spheres, Bull Amer. Math. Soc., 78, (1972), 593-596. Zbl0279.53055MR298590
  17. [17] H. Toda, Composition Methods in Homotopy Groups of Spheres, Annals of Mathematics Studies49, Princeton, (1962). Zbl0101.40703MR143217
  18. [18] G. Toth, Harmonic and minimal maps with applications in geometry and physics, E. Horwood, (1984). Zbl0545.58003MR770205

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