On the sectional curvature along central configurations

Connor Jackman; Josué Meléndez

doi:10.1134/s1560354718070109

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arXiv · 1703.08445

On the sectional curvature along central configurations

Connor Jackman·Josué Meléndez

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Abstract

In this paper we characterize planar central configurations in terms of a sectional curvature value of the Jacobi-Maupertuis metric. This characterization works for the $N$-body problem with general masses and any $1/r^{\alpha}$ potential with $\alpha> 0$. We also observe dynamical consequences of these curvature values for relative equilibrium solutions. These curvature methods work well for strong forces ($\alpha \ge 2$).

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Connor Jackman, Josué Meléndez. 2017-03-24. On the sectional curvature along central configurations. https://doi.org/10.1134/s1560354718070109

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