Coset spaces and Einstein manifolds with l-conformal Galilei symmetry

TL;DR

This paper constructs Einstein metrics with $l$-conformal Galilei symmetry using group theory, revealing novel geodesic dynamics on coset spaces with independent integrals of motion.

Contribution

It introduces a new dynamical realization of the $l$-conformal Galilei group via geodesics on coset spaces and extends analysis to Einstein metrics with this symmetry.

Findings

Geodesics have functionally independent integrals of motion.

Constructed Einstein metrics with $l$-conformal Galilei isometry.

Extended previous work to include Einstein metrics with this symmetry.

Abstract

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 [Phys. Lett. B 754 (2016) 249] is extended to construct the Einstein metrics with the $l$--conformal Galilei isometry group.