Coset spaces and Einstein manifolds with \(l\)-conformal Galilei symmetry. (English) Zbl 1346.53048
Summary: 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 [the author and A. Galajinsky, Phys. <lett. B 754, 264-269 (2016; doi:10.1016/j.phys.letb.2016.01.037)] is extended to construct the Einstein metrics with the \(l\)-conformal Galilei isometry group.
MSC:
| 53C25 | Special Riemannian manifolds (Einstein, Sasakian, etc.) |
| 53C22 | Geodesics in global differential geometry |
| 22E70 | Applications of Lie groups to the sciences; explicit representations |
| 81T25 | Quantum field theory on lattices |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
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