Almost symplectic structures and harmonic morphisms

Jean-Marie Burel

Bollettino dell'Unione Matematica Italiana (2004)

  • Volume: 7-B, Issue: 2, page 493-507
  • ISSN: 0392-4041

Abstract

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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.

How to cite

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Burel, Jean-Marie. "Almost symplectic structures and harmonic morphisms." Bollettino dell'Unione Matematica Italiana 7-B.2 (2004): 493-507. <http://eudml.org/doc/195718>.

@article{Burel2004,
abstract = {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.},
author = {Burel, Jean-Marie},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {493-507},
publisher = {Unione Matematica Italiana},
title = {Almost symplectic structures and harmonic morphisms},
url = {http://eudml.org/doc/195718},
volume = {7-B},
year = {2004},
}

TY - JOUR
AU - Burel, Jean-Marie
TI - Almost symplectic structures and harmonic morphisms
JO - Bollettino dell'Unione Matematica Italiana
DA - 2004/6//
PB - Unione Matematica Italiana
VL - 7-B
IS - 2
SP - 493
EP - 507
AB - 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.
LA - eng
UR - http://eudml.org/doc/195718
ER -

References

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  1. BAIRD, P.- EELLS, J., A conservation law for harmonic maps, Geometry Symp. Utrecht (1980), Springer Notes, 894 (1981), 1-25. Zbl0485.58008MR655417
  2. BAIRD, P.- GUDMUNDSSON, S., p -harmonic maps and minimal submanifolds, Math. Ann., 294 (1992), 611-624. Zbl0757.53031MR1190447
  3. BAIRD, P.- OU, Y.-L., Harmonic maps and morphisms from multilinear norm-preserving mappings, International. J. Math. Volume 8, 2 (1997), 187-211. Zbl0885.58013MR1442435
  4. BUREL, J.-M., Applications et morphismes harmoniques à valeurs dans une surface, Comptes Rendus de l'Académie des Sciences, Paris, t.332, Série I (2001), 441-446. Zbl1040.58005MR1826632
  5. EELLS, J.- FERREIRA, M. J., On representing homotopy classes by harmonic maps, Bull. Lond. Math. Soc, 23, no. 2 (1991), 160-162. Zbl0704.58014MR1122903
  6. FUGLEDE, B., Harmonic morphisms between Riemannian manifolds, Ann. Inst. Fourier, 28 (1978), 107-144. Zbl0339.53026MR499588
  7. GROMOV, M., Pseudo holomorphic curves in symplectic manifolds, Invent. Math., 82 (1985), 307-347. Zbl0592.53025
  8. ISHIHARA, T., A mapping of Riemannian manifolds which preserves harmonic functions, J. Math. Kyoto. Univ., 19 (1979), 215-229. Zbl0421.31006MR545705
  9. MO, X., 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). Zbl0952.53031MR1735681
  10. PANTILIE, R., Harmonic morphisms with one dimensional fibres, International. J. Math., 10 (1999), 457-501. Zbl0966.53044MR1697618
  11. VILLE, M., Harmonic morphisms from Einstein 4 -manifolds to Riemann surfaces, Internat. J. Math., 14 (2003), 327-337. Zbl1067.53052MR1978451

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