Jacobi-Maupertuis-Eisenhart metric and geodesic flows
  The Jacobi metric derived from the line element by one of the authors is shown to reduce to the standard formulation in the non-relativistic approximation. We obtain the Jacobi metric for various stationary metrics. Finally, the Jacobi-Maupertuis metric is formulated for time-dependent metrics by including the Eisenhart-Duval lift, known as the Jacobi-Eisenhart metric. 
Sumanto Chanda, G.W. Gibbons, Partha Guha
math-ph gr-qc math.MP