Tohoku Mathematical Journal

Pinching and nonexistence of stable harmonic maps

Takashi Okayasu

Full-text: Open access

Article information

Tohoku Math. J. (2), Volume 40, Number 2 (1988), 213-220.

First available in Project Euclid: 3 May 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 58E20: Harmonic maps [See also 53C43], etc.
Secondary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]


Okayasu, Takashi. Pinching and nonexistence of stable harmonic maps. Tohoku Math. J. (2) 40 (1988), no. 2, 213--220. doi:10.2748/tmj/1178228027.

Export citation


  • [1] K. GROVE, H. KARCHER AND E. A. RUH, Jacobi fields and Finsler metrics on compact Lie groups with an application to differentiable pinching problems, Math. Ann. 211 (1974), 7-21.
  • [2] K. GROVE, H. KARCHER AND E. A. RUH, Group actions and curvature, Inv. Math. 2 (1974), 31-48.
  • [3] R. HOWARD, The nonexistence of stable submanifolds, varifolds, and harmonic maps i sufficiently pinched simply connected Riemannian manifolds, Mich. Math. J. 32 (1985). 321-334.
  • [4] R. HOWARD AND S. W. WEI, Nonexistence of stable harmonic maps to and from certai homogeneous spaces and submanifolds of Euclidean space, Trans. Amer. Math. Soc. 294 (1986), 319-331.
  • [5] H. B. LAWSON AND J. SIMONS, On stable currents and their application to global problem in real and complex geometry, Ann. of Math. (2) 98 (1973), 427-450.
  • [6] P. F. LEUNG, On the stability of harmonic maps, Lecture Notes in Mathematics 949, Springer-Verlag, Berlin, Heidelberg, New York, 1982, 122-129.
  • [7] P. F. LEUNG, A note on stable harmonic maps, J. London Math. Soc. (2) 29 (1984), 380-384
  • [8] Y. OHNITA, Stability of harmonic maps and standard minimal immersions, Thoku Math J. 38 (1986), 259-267.