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Harmonicity of Holomorphic Maps Between Almost Hermitian Manifolds

Published online by Cambridge University Press:  20 November 2018

Domingo Chinea*
Affiliation:
Department of Fundamental Mathematics, University of La Laguna, Tenerife, Spain e-mail: dchinea@ull.es
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Abstract

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In this paper we study holomorphic maps between almost Hermitian manifolds. We obtain a new criterion for the harmonicity of such holomorphic maps, and we deduce some applications to horizontally conformal holomorphic submersions.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2009

References

[1] Baird, P. and Eells, J., A conservation law for harmonic maps. Geometry Symposium Utrecht 1980, In: Lecture Notes in Math. 894, Springer, Berlin-New York, 1981, pp. 125.Google Scholar
[2] Fuglede, B., Harmonic morphisms between Riemannian manifolds. Ann. Inst. Fourier 28(1978), no. 2, 107144.Google Scholar
[3] Eells, J. and Sampson, J. H., Harmonic mappings of Riemannian manifolds. Amer. J. Math. 86(1964), 109160.Google Scholar
[4] Gray, A. and Hervella, L. M., The sixteen classes of almost Hermitian manifolds and their linear invariant. Ann. Mat. Pura Appl. 123(1980), 3558.Google Scholar
[5] Gudmundsson, S. The geometry of harmonic morphisms. Ph.D. Thesis, University of Leeds (1992).Google Scholar
[6] Gudmundsson, S. and Wood, J. C., Harmonic morphisms between almost Hermitian manifolds. Boll. Un. Mat. Ital. B(7) 11(1997), no. 2, suppl., 185197.Google Scholar
[7] Ishihara, T., A mapping of Riemannian manifolds which preserves harmonic functions. J. Math. Kyoto Univ. 19(1979), 215229.Google Scholar
[8] Lichnerowicz, A., Applications harmoniques et variétés kähleriennes. In: 1968/1969 Symposia Mathematica, Vol. III, Academic Press, London, 1970, pp. 341402.Google Scholar
[9] O’Neill, B., The fundamental equations of a submersion. MichiganMath. J. 13(1966), 459469.Google Scholar
[10] Watson, B., Almost Hermitian submersions. J. Differential Geometry 11(1976), no. 1, 147165.Google Scholar
[11] Watson, B. and Vanhecke, L., The structure equation of an almost semi-Kähler submersion. Houston J. Math. 5(1979), no. 2, 295305.Google Scholar