Harmonicity of Holomorphic Maps Between Almost Hermitian Manifolds
Canadian mathematical bulletin, Tome 52 (2009) no. 1, pp. 18-27

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2009-003-4
Mots-clés : 53C15, 58E20, almost Hermitian manifolds, harmonic maps, harmonic morphism
Chinea, Domingo. Harmonicity of Holomorphic Maps Between Almost Hermitian Manifolds. Canadian mathematical bulletin, Tome 52 (2009) no. 1, pp. 18-27. doi: 10.4153/CMB-2009-003-4
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[1] [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] [2] Fuglede, B., Harmonic morphisms between Riemannian manifolds. Ann. Inst. Fourier 28(1978), no. 2, 107–144. Google Scholar

[3] [3] Eells, J. and Sampson, J. H., Harmonic mappings of Riemannian manifolds. Amer. J. Math. 86(1964), 109–160. Google Scholar

[4] [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] [5] Gudmundsson, S. The geometry of harmonic morphisms. Ph.D. Thesis, University of Leeds (1992). Google Scholar

[6] [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] [7] Ishihara, T., A mapping of Riemannian manifolds which preserves harmonic functions. J. Math. Kyoto Univ. 19(1979), 215–229. Google Scholar

[8] [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] [9] O’Neill, B., The fundamental equations of a submersion. MichiganMath. J. 13(1966), 459–469. Google Scholar

[10] [10] Watson, B., Almost Hermitian submersions. J. Differential Geometry 11(1976), no. 1, 147–165. Google Scholar

[11] [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

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