Relative equilibria in curved restricted 4-body problems

Abstract

We consider the curved 4-body problems on spheres and hyperbolic spheres. After obtaining a criterion for the existence of quadrilateral configurations on the equator of the sphere, we study two restricted 4-body problems, one in which two masses are negligible and another in which only one mass is negligible. In the former, we prove the evidence square-like relative equilibria, whereas in the latter we discuss the existence of kite-shaped relative equilibria.