Method of dimensional regularization for scalar and vector fields in homogeneous isotropic spaces

A consistent analytic continuation of the relations of the theory of quantized scalar (with arbitrary coupling) and vector fields in isotropic metrics into the complex plane with respect to the number of space-time dimensions is constructed. Dimensionally regularized values are obtained for the quantities subtracted from the vacuum energy-momentum tensor when the divergences are eliminated, and their geometrical structure is established. All the infinite subtractions are interpreted in terms of renormalizations.