Angular momenta of relative equilibrium motions and real moment map geometry

• 成果类型: Article
• 署名作者: Heckman, Gert; Zhao, Lei
• 署名单位: Radboud University Nijmegen; Nankai University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-015-0644-2
• 发表日期: 2016
• 页码: 671-691
• 关键词: convexity properties; n bodies

摘要

Chenciner and Jim,nez-P,rez (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.