ABSTRACT
First we present a brief comparison between several methods which have been used in the literature to show why Riemannian geometry is necessary for control of the wave equation with variable coefficients. Then we generalize the classical multipliers ([39], [40], [41], [86], [99], [104], [105], [117]-[122], [146], and many others) in a version of the Riemannian geometry setting with help of the Bochner technique to find out verifiable, geometric assumptions for control of the wave equation with variable coefficients in space. Controllability/stabilization of the wave equation with variable coefficients comes down to an escape vector field for the Riemannian metric, given by the variable coefficients.
