  In a previous paper, field theory in curved space was considered, and a
formula that expresses the first order variation of correlation functions with
respect to the external metric was postulated. The formula is given as an
integral of the energy-momentum tensor over space, where the short distance
singularities of the product of the energy-momentum tensor and an arbitrary
composite field must be subtracted, and finite counterterms must be added.
These finite counterterms have been interpreted geometrically as a connection
for the linear space of composite fields over theory space. In this paper we
will study a second order consistency condition for the variational formula and
determine the torsion of the connection. A non-vanishing torsion results from
the integrability of the variational formula, and it is related to the Bose
symmetry of the product of two energy-momentum tensors. The massive Ising model
on a curved two-dimensional surface is discussed as an example, and the
short-distance singularities of the product of two energy-momentum tensors are
calculated explicitly.
