Null Surfaces and Legendre Submanifolds
arXiv:gr-qc/9805027 · doi:10.1063/1.533077
Abstract
It is shown that the main variable Z of the Null Surface Formulation of GR is the generating function of a constrained Lagrange submanifold that lives on the energy surface H=0 and that its level surfaces Z=const. are Legendre submanifolds on that energy surface. The behaviour of the variable Z at the caustic points is analysed and a genralization of this variable is discussed.
28 pages, 7 figures