Indice de Morse des applications harmoniques de la sphère

Ahmad El Soufi

Compositio Mathematica (1995)

  • Volume: 95, Issue: 3, page 343-362
  • ISSN: 0010-437X

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El Soufi, Ahmad. "Indice de Morse des applications harmoniques de la sphère." Compositio Mathematica 95.3 (1995): 343-362. <http://eudml.org/doc/90354>.

@article{ElSoufi1995,
author = {El Soufi, Ahmad},
journal = {Compositio Mathematica},
keywords = {Morse index; harmonic maps; sphere; instability degree; canonical inversion index; smallest index},
language = {fre},
number = {3},
pages = {343-362},
publisher = {Kluwer Academic Publishers},
title = {Indice de Morse des applications harmoniques de la sphère},
url = {http://eudml.org/doc/90354},
volume = {95},
year = {1995},
}

TY - JOUR
AU - El Soufi, Ahmad
TI - Indice de Morse des applications harmoniques de la sphère
JO - Compositio Mathematica
PY - 1995
PB - Kluwer Academic Publishers
VL - 95
IS - 3
SP - 343
EP - 362
LA - fre
KW - Morse index; harmonic maps; sphere; instability degree; canonical inversion index; smallest index
UR - http://eudml.org/doc/90354
ER -

References

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  1. [1] Bums, D., Burstall, F., de Bartolomeis, P. and Rawnsley, J., Stability of harmonie maps of Kähler manifolds, J. Diff. Geom.30 (1989) 579-594. Zbl0678.53062MR1010173
  2. [2] Eells, J. and Lemaire, L., Selected topics in harmonie maps, C.B.M.S. Regional Conf. Ser.50, A.M.S., Providence (1983). Zbl0515.58011MR703510
  3. [3] Eells, J. and Lemaire, L., A report on harmonie maps, Bull. London Math. Soc.10 (1978) 1-68. Zbl0401.58003MR495450
  4. [4] El Soufi, A., Applications harmoniques, immersions minimales et transformations conformes de la sphère, Compositio Math.85(3) (1993). Zbl0777.58010MR1214448
  5. [5] El Soufi, A. and Ilias S., Immersions minimales, première valeur propre du Laplacien et volume conforme, Math. Ann.275 (1986) 257-267. Zbl0675.53045MR854009
  6. [6] El Soufi, A. and Ilias, S., Une inégalité du type "Reilly" pour les sous-variétés de l'espace hyperbolique, Comment. Math. Helv.67 (1992) 167-181. Zbl0758.53029MR1161279
  7. [7] Ferreira, M.J., Morse indices for certain harmonie maps of surfaces, Bull Soc. Math. Belg.B36 (1984) 131-153. Zbl0561.58010MR777193
  8. [8] Gallot, S. and Meyer, D., Opérateur de courbure et Laplacien des formes différentielles d'une variété riemannienne, J. Math. Pures Appl.54 (1975) 259-289. Zbl0316.53036MR454884
  9. [9] Iwasaki, I. and Katase, K., On the spectra of Laplace operator on Λ*(Sn), Proc. Japan. Acad.55, A (1979) 141-145. Zbl0442.58029
  10. [10] Lawson, H.B. and Simons, J., On stable currents and their application to global problems in real and complex geometry, Ann. of Math.98(2) (1973) 427-450. Zbl0283.53049MR324529
  11. [11] Lichnerowicz, A., Applications harmoniques et variétés Kählériennes, Sympos. Math.3 (1970) 341-402. Zbl0193.50101MR262993
  12. [12] Ohnita, Y. and Udagawa, S., Stability of harmonie maps from Riemann surfaces to compact Hermitian symmetric spaces, Tokyo J. Math.10 (1987) 385-390. Zbl0646.58019MR926250
  13. [13] Ramanathan, J., A remark on the energy of harmonie maps between spheres, Roky Mountain J. Math.16 (1986) 783-790. Zbl0611.58022MR871035
  14. [14] Simons, J., Minimal varieties in Riemannian manifolds, Ann. of Math.88 (1968) 62-105. Zbl0181.49702MR233295
  15. [15] Siu, Y.T., The complex analyticity of harmonie maps and the strong rigidity of compact Kähler manifolds, Ann. of Math.112(2) (1980) 73-111. Zbl0517.53058MR584075
  16. [16] Siu, Y.T., Yau, S.T., Compact Kähler manifolds of positive bisectional curvature, Invent. Math.59 (1980) 189-204. Zbl0442.53056MR577360
  17. [17] Smith, R.T., The second variation formula for harmonie mappings, Proc. Am. Math. Soc.47 (1975) 229-236. Zbl0303.58008MR375386
  18. [18] Urakawa, H., Stability of harmonie maps and eigenvalues of the Laplacian, Trans. Amer. Math. Soc.301 (1987) 557-589. Zbl0621.58010MR882704
  19. [19] Xin, Y.L., Some results on stable harmonie maps, Duke Math. J.47 (1980) 609-613. Zbl0513.58019MR587168

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