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Harmonic Almost Contact Structures

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Abstract

An almost contact metric structure is parametrized by a section σ of an associated homogeneous fibre bundle, and conditions for σ to be a harmonic section, and a harmonic map, are studied. These involve the characteristic vector field ξ, and the almost complex structure in the contact subbundle. Several examples are given where the harmonic section equations for σ reduce to those for ξ, regarded as a section of the unit tangent bundle. These include trans-Sasakian structures. On the other hand, there are examples where ξ is harmonic but σ is not a harmonic section. Many examples arise by considering hypersurfaces of almost Hermitian manifolds, with the induced almost contact structure, and comparing the harmonic section equations for both structures.

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Authors and Affiliations

  1. School of Mathematics, Trinity College Dublin, Dublin 2, Ireland

    E. Vergara-Diaz

  2. Department of Mathematics, University of York, Heslington, York, Y010 5DD, UK

    C. M. Wood

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  1. E. Vergara-Diaz
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  2. C. M. Wood
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Correspondence to E. Vergara-Diaz.

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Vergara-Diaz, E., Wood, C.M. Harmonic Almost Contact Structures. Geom Dedicata 123, 131–151 (2006). https://doi.org/10.1007/s10711-006-9112-x

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  • DOI: https://doi.org/10.1007/s10711-006-9112-x

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