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Harmonic almost contact structures. (English) Zbl 1118.53043

Author’s abstract: An almost contact metric structure is parametrized by a section \(\sigma\) of an associated homogeneous fibre bundle, and conditions for \(\sigma\) to be a harmonic section, and a harmonic map, are studied. These involve the characteristic vector field \(\xi\) and the almost complex structure in the contact subbundle. Several examples are given where the harmonic section equations for \(\sigma\) reduce to those for \(\xi\), regarded as a section of the unit tangent bundle. These include trans-Sasakian structures. On the other hand, there are examples where \(\xi\) is harmonic but \(\sigma\) 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.

MSC:

53C43 Differential geometric aspects of harmonic maps
53C56 Other complex differential geometry
53D10 Contact manifolds (general theory)
53D15 Almost contact and almost symplectic manifolds
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References:

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