Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The index of a holomorphic mapping and the index theorem

Author: Tôru Ishihara
Journal: Proc. Amer. Math. Soc. 66 (1977), 169-174
MSC: Primary 58E15; Secondary 53C20
MathSciNet review: 0494249
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The index theorem for a harmonic mapping of riemannian manifolds is given. Let $ f:M \to N$ be a holomorphic mapping of Kaehler manifolds. Then it is shown that the index of f is zero and that a Jacobi field along f is a holomorphic section of the bundle $ {f^ \ast }T(N)$ induced by f.

References [Enhancements On Off] (What's this?)

  • [1] S. I. Goldberg and T. Ishihara, Harmonic quasiconformal mappings of riemannian manifolds, Bull. Amer. Math. Soc. 80 (1974), 562-566. MR 0341335 (49:6086)
  • [2] S. I. Goldberg, T. Ishihara and N. C. Petridis, Mappings of bounded dilatation of riemannian manifolds, J. Differential Geometry 10 (1975), 619-630. MR 0390964 (52:11787)
  • [3] A. Lichnerowicz, Applications harmoniques et variétés kahleriennes, Rend. Sem. Mat. Fis. Milano 39 (1969), 1-12. MR 0270305 (42:5195)
  • [4] E. Mazet, La formule de la variation seconde de l'energie au voisinage d'une application harmonique, J. Differential Geometry 8 (1973), 279-296. MR 0336767 (49:1540)
  • [5] J. Simons, Minimal varieties in riemannian manifolds, Ann. of Math. (2) 88 (1968), 62-105. MR 0233295 (38:1617)
  • [6] S. Smale, On the Morse index theorem, J. Math. Mech. 14 (1965), 1049-1056. MR 0182027 (31:6251)
  • [7] R. T. Smith, The second variation formula for harmonic mappings, Proc. Amer. Math. Soc. 47 (1975), 229-236. MR 0375386 (51:11580)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58E15, 53C20

Retrieve articles in all journals with MSC: 58E15, 53C20

Additional Information

Keywords: Harmonic mapping, index, holomorphic mapping
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society