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Holomorphic harmonic morphisms from cosymplectic almost Hermitian manifolds

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Abstract

We study 4-dimensional orientable Riemannian manifolds equipped with a minimal and conformal foliation \({\mathcal {F}}\) of codimension 2. We prove that the two adapted almost Hermitian structures \(J_1\) and \(J_2\) are both cosymplectic if and only if \({\mathcal {F}}\) is Riemannian and its horizontal distribution \({\mathcal {H}}\) is integrable.

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References

  1. Baird, P., Eells, J.: A conservation law for harmonic maps. In: Geometry Symposium Utrecht 1980, Lecture Notes in Mathematics, vol. 894. Springer, Berlin, pp. 1–25 (1981)

  2. Baird, P., Wood, J.C.: Harmonic Morphisms Between Riemannian Manifolds, London Math. Soc. Monogr. No. 29. Oxford Universiyt Press, Oxford (2003)

    Book  Google Scholar 

  3. Fuglede, B.: Harmonic morphisms between Riemannian manifolds. Ann. Inst. Fourier 28, 107–144 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  4. Gudmundsson, S.: The Bibliography of Harmonic Morphisms, http://www.matematik.lu.se/matematiklu/personal/sigma/harmonic/bibliography.html

  5. Gudmundsson, S., Svensson, M.: Harmonic morphisms from four-dimensional Lie groups. J. Geom. Phys. 83, 1–11 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  6. Gudmundsson, S., Wood, J.C.: Harmonic morphisms between almost Hermitian manifolds. Boll. Un. Mat. Ital. (7) 11–B(Suppl. to fasc 1), 30–58 (1997)

    MathSciNet  Google Scholar 

  7. Ishihara, T.: A mapping of Riemannian manifolds which preserves harmonic functions. J. Math. Soc. Jpn. 7, 345–370 (1979)

    Article  Google Scholar 

  8. Lichnerowicz, A.: Applications harmoniques et variétés kählériennes. Sympos. Math. III, pp. 341–402 (INDAM, Rome 1968/69)

  9. Wood, J.C.: Harmonic morphisms and Hermitian structures on Einstein 4-manifolds. Int. J. Math. 3, 415–439 (1992)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Lund University, Box 118, 221 00, Lund, Sweden

    Sigmundur Gudmundsson

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  1. Sigmundur Gudmundsson
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Correspondence to Sigmundur Gudmundsson.

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Gudmundsson, S. Holomorphic harmonic morphisms from cosymplectic almost Hermitian manifolds. Geom Dedicata 178, 143–150 (2015). https://doi.org/10.1007/s10711-015-0049-9

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  • DOI: https://doi.org/10.1007/s10711-015-0049-9

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