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Angular momenta of relative equilibrium motions and real moment map geometry

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Chenciner and Jiménez-Pérez (Mosc Math J 13(4):621–630, 2013) showed that the range of the spectra of the angular momenta of all the rigid motions of a fixed central configuration in a general Euclidean space form a convex polytope. In this note we explain how this result follows from a general convexity theorem of O’Shea and Sjamaar in real moment map geometry (Math Ann 31:415–457, 2000). Finally, we provide a representation-theoretic description of the pushforward of the normalized measure under the real moment map for Riemannian symmetric pairs.

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Authors and Affiliations

  1. Radboud University, Nijmegen, The Netherlands

    Gert Heckman

  2. Chern Institute of Mathematics, Nankai University, Tianjin, People’s Republic of China

    Lei Zhao

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  1. Gert Heckman
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  2. Lei Zhao
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Correspondence to Lei Zhao.

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Heckman, G., Zhao, L. Angular momenta of relative equilibrium motions and real moment map geometry. Invent. math. 205, 671–691 (2016). https://doi.org/10.1007/s00222-015-0644-2

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