Almost symplectic structures and harmonic morphisms
Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 2, pp. 493-507.

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In this paper, we introduce the notion of symplectic harmonic maps between tamed manifolds and establish some properties. In the case where the manifolds are almost Hermitian manifolds, we obtain a new method to contruct harmonic maps with minimal fibres. We finally present examples of such applications between projectives spaces.
In questo articolo, introduciamo la nozione di applicazione armonica simplettica fra varietà addomesticate e otteniamo qualche proprietà. Nel caso in cui le varietà siano quasi hermitiane, otteniamo un nuovo metodo per costruire applicazioni armoniche con fibre minimali. In fine, presentiamo un esempio di tali applicazioni fra spazi proiettivi.
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Burel, Jean-Marie. Almost symplectic structures and harmonic morphisms. Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 2, pp. 493-507. http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_2_a14/

[1] P. Baird-J. Eells, A conservation law for harmonic maps, Geometry Symp. Utrecht (1980), Springer Notes, 894 (1981), 1-25. | MR | Zbl

[2] P. Baird-S. Gudmundsson, $p$-harmonic maps and minimal submanifolds, Math. Ann., 294 (1992), 611-624. | MR | Zbl

[3] P. Baird-Y.-L. Ou, Harmonic maps and morphisms from multilinear norm-preserving mappings, International. J. Math. Volume 8, 2 (1997), 187-211. | MR | Zbl

[4] J.-M. Burel, Applications et morphismes harmoniques à valeurs dans une surface, Comptes Rendus de l'Académie des Sciences, Paris, t.332, Série I (2001), 441-446. | MR | Zbl

[5] J. Eells-M. J. Ferreira, On representing homotopy classes by harmonic maps, Bull. Lond. Math. Soc, 23, no. 2 (1991), 160-162. | MR | Zbl

[6] B. Fuglede, Harmonic morphisms between Riemannian manifolds, Ann. Inst. Fourier, 28 (1978), 107-144. | fulltext mini-dml | MR | Zbl

[7] M. Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math., 82 (1985), 307-347. | Zbl

[8] T. Ishihara, A mapping of Riemannian manifolds which preserves harmonic functions, J. Math. Kyoto. Univ., 19 (1979), 215-229. | fulltext mini-dml | MR | Zbl

[9] X. Mo, Harmonic morphisms via deformation of metrics for horizontally conformal maps, in Harmonic Morphisms, Harmonic maps and related topics, Proceedings of a conference held in Brest, France 7th-11th of July 1997, 75-96, CRC Press (1999). | MR | Zbl

[10] R. Pantilie, Harmonic morphisms with one dimensional fibres, International. J. Math., 10 (1999), 457-501. | MR | Zbl

[11] M. Ville, Harmonic morphisms from Einstein $4$-manifolds to Riemann surfaces, Internat. J. Math., 14 (2003), 327-337. | MR | Zbl