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Two-dimensional Riemannian and Lorentzian geometries from second order ODEs

Emanuel Gallo
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Abstract

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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Emanuel Gallo. 2004-08-05. Two-dimensional Riemannian and Lorentzian geometries from second order ODEs. https://doi.org/10.1063/1.1806261

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