The guiding light of this monograph is a question easy to understand but difficult to
answer:{What is the shape of the universe? In other words, how do we measure the shortest …

We consider the gravitational motion of $ n $ point particles with masses $ m_1, m_2,\dots,
m_n> 0$ on surfaces of constant positive Gaussian curvature. Using stereographic …

Abstract We consider the $3 $-dimensional gravitational $ n $-body problem, $ n\ge 2$, in
spaces of constant Gaussian curvature $\kappa\ne 0$, ie on spheres ${\mathbb S} _\kappa …

We consider the motion of n point particles of positive masses that interact gravitationally on
the 2-dimensional hyperbolic sphere, which has negative constant Gaussian curvature …

We consider the gravitational motion of $ n $ point particles with masses $ m_1 $, $ m_2 $,
$\ldots $, $ m_n> 0$ on surfaces of constant Gaussian curvature. Based on the work of …

We consider the N-body problem of celestial mechanics in spaces of nonzero constant
curvature. Using the concept of effective potential, we define the moment of inertia for …

We provide the differential equations that generalize the Newtonian-body problem in the
context of constant curvature spaces and thus oòers a natural generalization of the …

We prove that the geometry of the 2-dimensional $ n $-body problem for spaces of constant
curvature $\kappa\neq 0$, $ n\geq 3$, does not allow for polygonal homographic solutions …

Stability of Fixed Points and Associated Relative Equilibria of the 3-Body Problem on $${\mathbb
{S}}^1$$ and $${\mathbb {S}}^2$$ | SpringerLink Skip to main content Advertisement …

We consider the motion of point masses given by a natural extension of Newtonian
gravitation to spaces of constant positive curvature, in which the gravitational attraction …