Almost contact structures and harmonic maps with minimal fibres

• Autores: Jean-Marie Burel
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 30, Nº 2, 2004, págs. 393-411
• Idioma: inglés
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• Resumen

  • We study a class of maps between almost contact metric manifolds. We characterize harmonicity in terms of differential forms which allows one to construct minimal submanifolds. This new approach allows us to reduce the second order problem of harmonicity to a first order problem. In particular we show that any map submersive almost everywhere from a 3-manifold to a surface that commutes with the contact structure on the domain and the complex structure on the codomain can be rendered harmonic by a suitable choice of the metric.