Abstract
A classical result of Riemannian geometry states that Jacobi fields along geodesics of a Riemannian manifold (Q, g) can be obtained as geodesies of the so-called «complete lift» of the metric g itself to the tangent bundle TQ. We show that this classical result is in fact a very simple consequence of a completely general theorem of Calculus of Variations.
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Casciaro, B., Francaviglia, M. A new variational characterization of Jacobi fields along geodesies. Annali di Matematica pura ed applicata 172, 219–228 (1997). https://doi.org/10.1007/BF01782613
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DOI: https://doi.org/10.1007/BF01782613