It is the only expression, I know, which is absolute. Curvature, as a condition of state of any surface at any specific given location on that surface, can be expressed without the presence of anything else, including this coordinate system. Curvature is therefore absolute. Because surfaces are not rigid and constantly flexing, thus undergoing variation, curvature is a variable condition of state. Further, it has always been anticipated in physics, that the variation of state is equivalent to system energy .
Energy is change in state, such as potential or kinetic energy.