In this paper,two different methods are given,by which the famous Arnowitt-Deser-Misner (ADM) constraint equations for Einstein's gravitational fields can be derived.One method is to construct an action of gravitational fields with a parameter in the specetimes of Lorentzian sgnature.Thus,ADM constraints with a parameter can be obtained and the familiar ADM constraint equations can be naturally derived by adjusting the value of this parameter.The other is to apply the double complex function theory to gravitational fields in Hamiltonian formulation.Hence,the double constraints can be obtained,in which the well-known ADM constraint equations are included as a special case.In addition,the Lorentzian and Euclidean gravitational theory can be expressed in a unified way by use of these two different methods.
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