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Physics  1998 

Null Surfaces and Legendre Submanifolds

DOI: 10.1063/1.533077

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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.

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