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Notation and preliminary remarks
A geometric approach to the calculus of variations
14 other sections not shown
2-form Q 6gij 6nij action functional admissible initial surface ADMW coordinate system ADMW density Adx3 boundary conditions bundle canonical Cauchy Cauchy data co-singular section co-singular submanifold components consider consists constraint equations 8.10b corresponding couple covector decomposition define definition denote depend determines dgij differential form differential operators Dissertationes Mathematicae dnij dx2A dx3 Einstein equations electrodynamics equations of motion equivalent exterior derivative form Q formula gauge distribution geometric gives gravidynamics Hamilton-Jacobi equation initial values Kijowski lagrangian Legendre transformation Lie algebra linearized equations mapping metric g metric tensor multiphase structure multisymplectic manifold neighbourhood obtain phase space physical quantities Poisson bracket problem Proof of Proposition proof see Section Proposition 8.1 represented by vector satisfying Section 15 smooth functionals space Jf space-like surface submanifold subset superphase space symplectic tangent space Tc(Jf tensor density tensor g Theorem transformation variational principle vector field virtue of Proposition XeTc(Jf