Abstract
We prove the existence of many homographic solutions of the n-body problem in E 4 by topological methods. Homographic solutions are associated with relative equilibria. Homothetic solutions always give rise to central configurations. In Euclidean space E 4 central configurations are a proper subset of the relative equilibria for any n ⩾ 3 and for any ( m i ) ϵR + n . We compare the existence and classification of homographic solutions of the n-body problem in E 3 with the Newtonian potential and that of homographic solutions of the n-body problem in E 4. Classifying relative equilibria leads to classifying homographic solutions.
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