Differential Geometry from Differential Equations

Details Differential Geometry from Differential Equations Differential Geometry from Differential Equations

Dec 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002nmgm.meet..805f&link_type=abstract

"THE NINTH MARCEL GROSSMANN MEETING On Recent Developments in Theoretical and Experimental General Relativity, Gravitation and R

Physics

Scientific paper

Cartan and followers showed, in the 1930's, how certain geometric structures can be associated with third-order ordinary differential equations. These geometric structures include a three-dimensional spacetime with a Lorentzian conformal metric. Here we show how Cartan's perspective can be generalized in order to treat pairs of second order partial differential equations (PDE) in two variables. In particular, we show that a four-dimensional spacetime with a conformal Lorentzian metric is associated with such pairs of PDE's.

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