Two-dimensional Riemannian and Lorentzian geometries from second order ODEs

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.

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

References in corpus (2)

• Differential Geometry from Differential Equations
• Cartan Normal Conformal Connections from Pairs of 2nd Order PDE's

Cited by in corpus (1)

• N-dimensional geometries and Einstein equations from systems of PDE's