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arxiv: 0711.3703 · v1 · submitted 2007-11-23 · 🧮 math.DG

Harmonicity of sections of sphere bundles

J.C. Gonzalez-Davila , F. Martin Cabrera , M. Salvai This is my paper
classification 🧮 math.DG
keywords sectionsspherebundleequippedharmonicmethodadequatebundles
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We consider the energy functional on the space of sections of a sphere bundle over a Riemannian manifold (M, <,>) equipped with the Sasaki metric and we discuss the characterising condition for critical points. Likewise, 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 <,>. This leads to the construction of a lot of new examples of differential forms which are harmonic sections or determine a harmonic map from (M,<,>) into its sphere bundle.

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  1. Harmonic almost contact metric manifolds revisited

    math.DG 2019-07 unverdicted novelty 4.0

    Generalizes harmonicity characterizations for almost contact metric manifolds and maps using intrinsic torsion in a more general setting.