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Harmonicity of Holomorphic Maps Between Almost Hermitian Manifolds

Published online by Cambridge University Press:  20 November 2018

Domingo Chinea
Domingo Chinea*
Affiliation:
Department of Fundamental Mathematics, University of La Laguna, Tenerife, Spain e-mail: [email protected]
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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.

Keywords

53C1558E20almost Hermitian manifoldsharmonic mapsharmonic morphism
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 52 , Issue 1 , 01 March 2009 , pp. 18 - 27
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. 1–25.Google Scholar
[2] Fuglede, B., Harmonic morphisms between Riemannian manifolds. Ann. Inst. Fourier 28(1978), no. 2, 107–144.Google Scholar
[3] Eells, J. and Sampson, J. H., Harmonic mappings of Riemannian manifolds. Amer. J. Math. 86(1964), 109–160.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), 35–58.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., 185–197.Google Scholar
[7] Ishihara, T., A mapping of Riemannian manifolds which preserves harmonic functions. J. Math. Kyoto Univ. 19(1979), 215–229.Google Scholar
[8] Lichnerowicz, A., Applications harmoniques et variétés kähleriennes. In: 1968/1969 Symposia Mathematica, Vol. III, Academic Press, London, 1970, pp. 341–402.Google Scholar
[9] O’Neill, B., The fundamental equations of a submersion. MichiganMath. J. 13(1966), 459–469.Google Scholar
[10] Watson, B., Almost Hermitian submersions. J. Differential Geometry 11(1976), no. 1, 147–165.Google Scholar
[11] Watson, B. and Vanhecke, L., The structure equation of an almost semi-Kähler submersion. Houston J. Math. 5(1979), no. 2, 295–305.Google Scholar