Morse indices of Yang-Mills connections over the unit sphere

Shin Nayatani; Hajime Urakawa

Compositio Mathematica (1995)

  • Volume: 98, Issue: 2, page 177-192
  • ISSN: 0010-437X

How to cite


Nayatani, Shin, and Urakawa, Hajime. "Morse indices of Yang-Mills connections over the unit sphere." Compositio Mathematica 98.2 (1995): 177-192. <>.

author = {Nayatani, Shin, Urakawa, Hajime},
journal = {Compositio Mathematica},
keywords = {Yang-Mills connection; weakly stable; Morse index},
language = {eng},
number = {2},
pages = {177-192},
publisher = {Kluwer Academic Publishers},
title = {Morse indices of Yang-Mills connections over the unit sphere},
url = {},
volume = {98},
year = {1995},

AU - Nayatani, Shin
AU - Urakawa, Hajime
TI - Morse indices of Yang-Mills connections over the unit sphere
JO - Compositio Mathematica
PY - 1995
PB - Kluwer Academic Publishers
VL - 98
IS - 2
SP - 177
EP - 192
LA - eng
KW - Yang-Mills connection; weakly stable; Morse index
UR -
ER -


  1. [BL] J.P. Bourguignon and H.B. Lawson, Stability and isolation phenomena for Yang-Mills fields, Commun. Math. Phys.79 (1981), 189-230. Zbl0475.53060MR612248
  2. [E1] A. El Soufi, Applications harmoniques, immersions minimales et transformations conformes de la sphère, Compositio Mathematica85 (1993), 281-298. Zbl0777.58010MR1214448
  3. [E2] A. El Soufi, Indice de Morse des applications harmoniques de la sphere, to appear in Compositio Mathematica. MR1318092
  4. [EI] A. El Soufi and S. Ilias, Une inégalité du type "Reilly" pour les sous-variétés de l'espace hyperbolique, Comment. Math. Helv.67 (1992), 167-181. Zbl0758.53029MR1161279
  5. [KN] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, vol. I, John Wiley and Sons, New York, 1963. Zbl0119.37502MR1393940
  6. [KOT] S. Kobayashi, Y. Ohnita and M. Takeuchi, On instability of Yang-Mills connections, Math. Zeit.193 (1986), 165-189. Zbl0634.53022MR856147
  7. [L] H.T. Laquer, Stability properties of the Yang-Mills functional near the canonical connection, Michigan Math. Jour.31 (1984), 139-159. Zbl0647.53022MR752251
  8. [O] M. Obata, Conformal transformations of Riemannian manifolds, Jour. Differential Geom.4 (1970), 311-333. Zbl0205.52003MR267485
  9. [S] R.T. Smith, The second variation formula for harmonic mappings, Proc. Amer. Math. Soc.47 (1975), 229-236. Zbl0303.58008MR375386
  10. [U] H. Urakawa, Stability of harmonic maps and eigenvalues of Laplacian, Trans. Amer. Math. Soc.301 (1987), 557-589. Zbl0621.58010MR882704
  11. [X] Y.L. Xin, Some remarks on stable harmonic maps, Duke Math. Jour.47 (1980), 609-613. Zbl0513.58019MR587168

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