The generalized curvature and Christoffel symbols for a higher spin potential in AdSd+1AdSd+1 space

The generalized curvature tensor and Christoffel symbols are determined in AdSd+1AdSd+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.