Equivariant harmonic maps between manifolds with metrics of ( p , q ) -signature

Andrea Ratto

Annales de l'I.H.P. Analyse non linéaire (1989)

  • Volume: 6, Issue: 6, page 503-524
  • ISSN: 0294-1449

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Ratto, Andrea. "Equivariant harmonic maps between manifolds with metrics of $(p, q)$-signature." Annales de l'I.H.P. Analyse non linéaire 6.6 (1989): 503-524. <http://eudml.org/doc/78189>.

@article{Ratto1989,
author = {Ratto, Andrea},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {hyperbolic systems; Lorentzian manifold; harmonic maps; Cauchy problem},
language = {eng},
number = {6},
pages = {503-524},
publisher = {Gauthier-Villars},
title = {Equivariant harmonic maps between manifolds with metrics of $(p, q)$-signature},
url = {http://eudml.org/doc/78189},
volume = {6},
year = {1989},
}

TY - JOUR
AU - Ratto, Andrea
TI - Equivariant harmonic maps between manifolds with metrics of $(p, q)$-signature
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1989
PB - Gauthier-Villars
VL - 6
IS - 6
SP - 503
EP - 524
LA - eng
KW - hyperbolic systems; Lorentzian manifold; harmonic maps; Cauchy problem
UR - http://eudml.org/doc/78189
ER -

References

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  2. [CB] Y. Choquet-Bruhat, Global Existence Theorems for Hyperbolic Maps, Ann. Inst. Henri Poincaré, Physique théorique, Vol. 46, 1987, pp. 97-111. Zbl0608.58018MR877997
  3. [EL1] J. Eells and L. Lemaire, A Report on Harmonic Maps, Bull. London Math. Soc., Vol. 10, 1978, pp. 1-68. Zbl0401.58003MR495450
  4. [EL2] J. Eells and L. Lemaire, Another Report on Harmonic Maps, Bull. London Math. Soc. (to appear). Zbl0669.58009MR956352
  5. [ES] J. Eells and J.H. Sampson, Harmonic mappings of riemannian manifolds, Am. J. Math., Vol. 86, 1964, pp. 109-160. Zbl0122.40102MR164306
  6. [GV] J. Ginibre and G. Velo, The Cauchy Problem for the O(N), C P(N-1) and G C(n, p) Models, Ann. Phys., Vol. 142, 1982, pp. 393-415. Zbl0512.58018MR678488
  7. [GU1] C.H. Gu, On the Cauchy Problem for Harmonic Maps Defined on Two Dimensional Minkowski Space, Commun. Pure Appl. Math., Vol. 33, 1980, pp. 727-737. Zbl0475.58005MR596432
  8. [GU2] C.H. Gu, On the Harmonic Maps from R1, 1 to S1, 1, J. Reine Ang. Math., Vol. 346, 1984, pp. 101-109. Zbl0513.58022MR727398
  9. [Ha] P. Hartman, Ordinary Differential Equations, Wiley, 1984. Zbl0125.32102MR171038
  10. [HL] J.X. Hong and J.Q. Liu, On Existence and Non-Existence of Some Harmonic Maps, Preprint, I.C.T.P., 1987. 
  11. [KW] H. Karcher and I.C. Wood, Non-Existence Results and Growth Properties for Harmonic Maps and Forms, J. Reine Angew. Math., Vol. 353, 1984, pp. 165-180. Zbl0544.58008MR765831
  12. [Le] J. Leray, Hyperbolic Differential Equations, I.A.S., Princeton, 1952. MR63548
  13. [Po] K. Pohlmeyer, Integrable Hamiltonian Systems and Interaction Through Quadratic Constrains, Commun. Math. Phys., Vol. 46, 1976, pp. 207-221. Zbl0996.37504MR408535
  14. [PR] V. Pettinati and A. Ratio, Existence and Non-Existence Results for Harmonic Maps Between Spheres, Ann. Sci. Norm. Sup. Pisa, to appear. Zbl0718.58017
  15. [R1] A. Ratto, Construction d'application harmoniques entre sphères euclidiennes, C.R. Acad. Sci. Paris, A304, Série A, 1987, pp. 185-186. Zbl0612.58014MR880922
  16. [R2] A. Ratto, Harmonic Maps of Spheres and Equivariant Theory, Ph. D. Thesis, Un. of Warwick, 1987. 
  17. [S1] R.T. Smith, Harmonic Mappings of Spheres, Amer. J. Math., Vol. 97, 1975, pp. 364-385. Zbl0321.57020MR391127
  18. [S2] R.T. Smith, Harmonic Mappings of Spheres, Ph. D. Thesis, Un. of Warwick, 1972. Zbl0279.53055MR298590
  19. [SW] R.K. Sachs and H. Wu,General Relativity for Mathematicians, Springer Verlag, Graduate texts in Math., Vol. 48, 1977. Zbl0373.53001MR503498

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