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

Abstract

The aim of the present work is twofold: first, we show how all the $n$-dimensional Riemannian and Lorentzian metrics can be constructed from a certain class of systems of second-order PDE's which are in duality to the Hamilton-Jacobi equation and second we impose the Einstein equations to these PDE's.

References in corpus (3)

• Differential Geometry from Differential Equations
• Cartan Normal Conformal Connections from Pairs of 2nd Order PDE's
• Two-dimensional Riemannian and Lorentzian geometries from second order ODEs