Coset spaces and Einstein manifolds with l-conformal Galilei symmetry

The group theoretic construction is applied to construct a novel dynamical realization of the l-conformal Galilei group in terms of geodesic equations on the coset space. A peculiar feature of the geodesics is that all their integrals of motion, including the accelerations, are functionally independent. The analysis in the recent work [Chernyavsky and Galajinsky (2016) [35]] is extended to construct the Einstein metrics with the l-conformal Galilei isometry group.