Two-dimensional Riemannian and Lorentzian geometries from second order ODEs

Details Two-dimensional Riemannian and Lorentzian geometries from second order ODEs Two-dimensional Riemannian and Lorentzian geometries from second order ODEs

2004-06-29

arxiv.org/abs/gr-qc/0406117v3

J.Math.Phys. 45 (2004) 4186-4190

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages, final version to appear in J. Math. Phys

Scientific paper

In this note we give an alternative geometrical derivation of the results recently presented by Garcia-Godinez, Newman and Silva-Ortigoza in [1] on the class of all two-dimensional riemannian and lorentzian metrics from 2nd order ODEs which are in duality with the two dimensional Hamilton-Jacobi equation. We show that, as it happens in the Null Surface Formulation of General Relativity, the Wuschmann-like condition can be obtained as a requirement of a vanishing torsion tensor. Furthermore, from these second order ODEs we obtain the associated Cartan connections.

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