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Harmonic maps and cosymplectic manifolds

Part of: Variational problems in infinite-dimensional spaces Global differential geometry

Published online by Cambridge University Press:  09 April 2009

E. Boeckx  and
C. Gherghe
E. Boeckx
Affiliation:
Katholieke Universiteit Leuven, Department of Mathematics Celestijnenlaan, 200B 3001 Leuven, Belgium e-mail: [email protected]
C. Gherghe
Affiliation:
University of Bucharest, Faculty of Mathematics Str. Academiei 14 70109 Bucharest, Romania, e-mail: [email protected]
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Abstract

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We study the harmonicity of maps to or from cosymplectic manifolds by relating them to maps to or from Kähler spaces.

Keywords

cosymplectic manifoldsharmonic mapsenergy(ϕ, J)-holomorphic maps, ϕ-pluriharmonic maps

MSC classification

Secondary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C43: Differential geometric aspects of harmonic maps 58E20: Harmonic maps , etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 76 , Issue 1 , February 2004 , pp. 75 - 92
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Blair, D. E., Contact manifolds in Riemannian geometry, Lecture Notes in Math. 509 (Springer, Berlin, 1976).CrossRefGoogle Scholar
[2]Capursi, M., ‘Some remarks on the product of two almost contact manifolds’, An. Şiinţ. Univ. Al. I. Cuza Iaşi Secţ. I a Mat. 30 (1984), 75–79.Google Scholar
[3]Eells, J. and Lemaire, L., ‘A report on harmonic maps’, Bull. London Math. Soc. 10 (1978), 1–68.CrossRefGoogle Scholar
[4]Eells, J. and Lemaire, L., Selected topics in harmonic maps, CBMS Regional Conference Series in Mathematics 50 (American Mathematical Society, Providence, 1983).CrossRefGoogle Scholar
[5]Eells, J. and Lemaire, L., ‘Another report on harmonic maps’, Bull. London Math. Soc. 20 (1988), 385–524.CrossRefGoogle Scholar
[6]Eells, J. and Sampson, J. H., ‘Harmonic mappings of Riemannian manifolds’, Amer. J. Math. 86 (1964), 109–160.CrossRefGoogle Scholar
[7]Fuglede, B., ‘Harmonic morphisms between Riemannian manifolds’, Ann. Inst. Fourier (Grenoble) 28 (1978), 107–144.CrossRefGoogle Scholar
[8]Gherghe, C., Ianus, S. and Pastore, A. M., ‘CR-manifolds, harmonic maps and stability’, J. Geom. 71 (2001), 42–53.CrossRefGoogle Scholar
[9]Gray, A. and Hervella, L. M., ‘The sixteen classes of almost Hermitian manifolds and their linear invariants’, Ann. Mat. Pura Appl. 123 (1980), 35–58.CrossRefGoogle Scholar
[10]Ianus, S. and Pastore, A. M., ‘Harmonic maps on contact metric manifolds’, Ann. Math. Blaise Pascal 2 (1995), 43–55.CrossRefGoogle Scholar
[11]Ishihara, T., ‘A mapping of Riemannian manifolds which preserves harmonic functions’, J. Math. Kyoto Univ. 19 (1979), 215–229.Google Scholar
[12]Loubeau, E., ‘Pluriharmonic morphisms between complex manifolds’, in: Differential geometry and applications (Brno, 1998) (Masaryk Univ., Brno, 1999) pp. 89–97.Google Scholar
[13]Mazet, E., ‘La formule de la variation seconde de l'énergie au voisinage d'une application harmonique’, J. Differential Geom. 9 (1974), 531–535.Google Scholar
[14]Morimoto, A., ‘On normal almost contact structures’, J. Math. Soc. Japan 15 (1963), 420–436.CrossRefGoogle Scholar
[15]Ohnita, Y. and Udagawa, S., ‘Complex-analyticity of pluriharmonic maps and their constructions’, in: Prospects in complex geometry (Katata and Kyoto, 1989), Lecture Notes in Math. 1468 (Springer, Berlin, 1991) pp. 371–407.CrossRefGoogle Scholar
[16]Oubiña, A., ‘New classes of almost contact metric structures’, Publ. Math. Debrecen 32 (1985), 187–193.CrossRefGoogle Scholar
[17]Siu, Y.-T., ‘The complex analyticity of harmonic maps and the strong rigidity of compact Kähler manifolds’, Ann. of Math. 112 (1980), 73–111.CrossRefGoogle Scholar
[18]Smith, R., ‘The second variation formula for harmonic mapping’, Proc. Amer. Math. Soc. 47 (1975), 229–236.CrossRefGoogle Scholar
[19]Tricerri, F. and Vanhecke, L., ‘Curvature tensors on almost Hermitian manifolds’, Trans. Amer. Math. Soc. 267 (1981), 365–398.CrossRefGoogle Scholar
[20]Udagawa, S., ‘Pluriharmonic maps and minimal immersions of Kähler manifolds’, J. London Math. Soc. 37 (1988), 375–384.CrossRefGoogle Scholar
[21]Urakawa, H., Calculus of variations and harmonic maps, Transl. Math. Monographs 132 (American Mathematical Society, Providence, 1993).Google Scholar
[22]Watson, B., ‘New examples of strictly almost Kählermanifolds’, Proc. Amer. Math. Soc. 88 (1983), 541–544.Google Scholar
[23]Yau, S. T., ‘A general Schwarz lemma for Kähler manifolds’, Amer. J. Math. 100 (1978), 197–203.CrossRefGoogle Scholar