  Space-Time in general relativity is a dynamical entity because it is subject
to the Einstein field equations. The space-time metric provides different
geometrical structures: conformal, volume, projective and linear connection. A
deep understanding of them has consequences on the dynamical role played by
geometry. We present a unified description of those geometrical structures,
with a standard criterion of naturalness, and then we establish relationships
among them and try to clarify the meaning of associated geometric magnitudes.
