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Harmonicity of sections of sphere bundles

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Abstract

We consider the energy functional on the space of sections of a sphere bundle over a Riemannian manifold \((M,\langle \cdot, \cdot \rangle)\) equipped with the Sasaki metric and discuss the characterising condition for critical points. Furthermore, we provide a useful method for computing the tension field in some particular situations. Such a method is shown to be adequate for many tensor fields defined on manifolds M equipped with a G-structure compatible with \(\langle \cdot, \cdot \rangle\) . This leads to the construction of several new examples of differential forms which are harmonic sections or determine a harmonic map from \((M,\langle \cdot, \cdot \rangle)\) into its sphere bundle.

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Authors and Affiliations

  1. Department of Fundamental Mathematics, University of La Laguna, 38200, La Laguna, Tenerife, Spain

    J. C. González-Dávila & F. Martín Cabrera

  2. Famaf-ciem, Ciudad Universitaria, 5000, Córdoba, Argentina

    M. Salvai

Authors
  1. J. C. González-Dávila
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  2. F. Martín Cabrera
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  3. M. Salvai
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Correspondence to F. Martín Cabrera.

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González-Dávila, J.C., Martín Cabrera, F. & Salvai, M. Harmonicity of sections of sphere bundles. Math. Z. 261, 409–430 (2009). https://doi.org/10.1007/s00209-008-0331-8

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  • DOI: https://doi.org/10.1007/s00209-008-0331-8

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