Relative Equilibria of the Curved N-Body Problem

Mehr zum Buch

Exploring the shape of the universe, this monograph addresses how to measure distances in physical space, questioning whether to follow straight lines or curved paths. It presents a mathematical proof that space is Euclidean for distances around 10 AU, confirming assumptions held by physicists. The work extends classical Newtonian gravitation into non-Euclidean spaces using the cotangent potential, originally proposed by Ernest Schering. This research uncovers intriguing connections among classical dynamics, non-Euclidean geometry, geometric topology, Lie groups, and polytopes.