Two dimensional Riemannian and Lorentzian geometries from second order ODEs

EMANUEL GALLO

JOURNAL OF MATHEMATICAL PHYSICS

AIP

Año: 2004 vol. 45 p. 4186 - 4190

0022-2488

In this paper we give an alternative geometrical derivation of the results recently presented by García-Godínez, Newman, and Silva-Ortigoza on the class of all two-dimensional Riemannian and Lorentzian metrics from second-order ODE?s 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 Wünschmann-type condition can be obtained as a requirement of a vanishing torsion tensor. Furthermore, from these second-order ODE?s we obtain the associated Cartan connections.