Abstract
This article demonstrates that in the Lobatchevsky space and on a sphere of arbitrary dimensions, the concept of the mass center of a system of mass points can be correctly defined. Presented are: a uniform geometric construction for defining the mass center; hyperbolic and spheric “lever rules”; the theorem of uniqueness for determining the mass center in these spaces. Among the compact manifolds, only the sphere possesses this property.
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Communicated by J. N. Mather
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Galperin, G.A. A concept of the mass center of a system of material points in the constant curvature spaces. Commun.Math. Phys. 154, 63–84 (1993). https://doi.org/10.1007/BF02096832
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DOI: https://doi.org/10.1007/BF02096832