The constraint equations in the presence of a scalar field: the case of the conformal method with volumetric drift (Q2291562)

The author applies the conformal method to determine the classical system of constraint equations and certain conditions are imposed on the presence of matter field. A priori estimates for solutions of the Lichnerowicz equation are also discussed. The conformal systems established by Maxwell in the presence of a scalar field and appropriate parameters are established. Further, in closed Riemannian manifolds of dimension 3, 4 and 5, metrics with and without conformal Killing fields are considered and some important results are established.