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Biharmonic holomorphic maps and conformally Kähler geometry

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Abstract

We give conditions on the Lee vector field of an almost Hermitian manifold such that any holomorphic map from this manifold into a (1, 2)-symplectic manifold must satisfy the fourth-order condition of being biharmonic, hence generalizing the Lichnerowicz theorem on harmonic maps. These third-order non-linear conditions are shown to greatly simplify on l.c.K. manifolds and construction methods and examples are given in all dimensions.

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Authors and Affiliations

  1. Département de Mathématiques, Université de Bretagne Occidentale, 6, avenue Victor Le Gorgeu, CS 93837, 29238, Brest Cedex 3, France

    M. Benyounes & E. Loubeau

  2. Department of Theoretical Physics and Mathematics, Faculty of Physics, University of Bucharest, P.O. Box Mg-11, RO-077125, Bucharest-Măgurele, Romania

    R. Slobodeanu

Authors
  1. M. Benyounes
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  2. E. Loubeau
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  3. R. Slobodeanu
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Corresponding author

Correspondence to M. Benyounes.

Additional information

The authors thank Liviu Ornea for many helpful comments on l.c.K. geometry. This article was written while the third author was invited professor at the University of Brest.

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Benyounes, M., Loubeau, E. & Slobodeanu, R. Biharmonic holomorphic maps and conformally Kähler geometry. Isr. J. Math. 201, 525–542 (2014). https://doi.org/10.1007/s11856-014-1029-z

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  • DOI: https://doi.org/10.1007/s11856-014-1029-z

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