  The generalized curvature tensor and Christoffel symbols are determined in
AdS_{d+1} background by a modified ansatz of the de Wit - Freedman type by
imposing gauge invariance. The resulting set of recurrence relations and
difference equations is solved. The Riemann curvature tensor is derived by
antisymmetrization. All results are presented as finite power series in the
inverse AdS radius and are unique. The fourth order, which is complete for
fields up to spin five, is calculated explicitly. Higher orders can be obtained
with the same method.
