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

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.