In accordance with the geometric Equivalence Principle, a world manifold possesses a Lorentzian structure, i.e., a structure group of a frame bundle F X must be reduced to a Lorentz group S O ( 1 , 3 ) . The corresponding global section of the quotient bundle F X / S O ( 1 , 3 ) is a pseudo-Riemannian metric g of signature ( + , − − − − − − ) on X . It is treated as a gravitational field in General Relativity and as a classical Higgs field in gauge gravitation theory.