Relativistic theory of gravimetric measurements and definition of the geoid.

Two different sets of level surfaces are introduced for an isolated gravitating body in a relativistic framework. The first set is defined by the rate of (ideal) atomic clocks (u level surfaces) , whereas each surface of the 2nd class is required to be orthogonal to the direction of the plumbline and to lie in the restspace of a comoving observer (a - level surfaces). These 2 bundles of level surfaces define what we call the u - and a - level surfaces (and corresponding geoids) coincide. The post - Newtonian theory of gravimetric measurements with parameters gamma and beta is presented with an accuracy of 10^-11g.-Authors