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The group theoretic construction is applied to construct a novel dynamicalrealization of the $l$--conformal Galilei group in terms of geodesic equationson the coset space. A peculiar feature of the geodesics is that all theirintegrals of motion, including the accelerations, are functionally independent.The analysis in the recent work [Phys. Lett. B 754 (2016) 249] is extended toconstruct the Einstein metrics with the $l$--conformal Galilei isometry group.

Coset spaces and Einstein manifolds with l-conformal Galilei symmetry