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• W1711897771 abstract "An n-body system is a labelled collection of n point masses in a Euclidean space, and their congruence and internal symmetry properties involve a rich mathematical structure which is investigated in the framework of equivariant Riemannian geometry. Some basic concepts are nconfiguration, configuration space, internal space, shape space, Jacobi transformation and weighted root system. The latter is a generalization of the root system of SU(n), which provides a bookkeeping for expressing the mutual distances of the point masses in terms of the Jacobi vectors. Moreover, its application to the study of collinear central n-configurations yields a simple proof of Moulton’s enumeration formula. A major topic is the study of matrix spaces representing the shape space of n-body configurations in Euclidean k-space, the structure of the m-universal shape space and its O(m)-equivariant linear model. This also leads to those “orbital fibrations” where SO(m) or O(m) act on a sphere with a sphere as orbit space. A few of these examples are encountered in the literature, e.g. the special case S 5 /O(2) ≈ S 4 was analyzed independently by Arnold, Kuiper and Massey in the 1970’s." @default.
• W1711897771 created "2016-06-24" @default.
• W1711897771 creator A5079962891 @default.
• W1711897771 date "2006-09-05" @default.
• W1711897771 modified "2023-09-27" @default.
• W1711897771 title "A geometric study of many body systems" @default.
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