Abstract We study the conditions for the existence of a sector with mass-degenerate supersymmetric partners in the presence of the spontaneous breaking of local supersymmetry, as the first step to characterize theories with residual global supersymmetry. The mass difference between fermions and scalars in each chiral multiplet is related to the Riemann curvatures tensor of the scalar field manifold, providing a necessary condition of geometrical nature on theories and chiral multiplets with degeneracy properties. From the study of the corresponding Riemann tensors, we determine the scalar curvature and the chiral multiplets consistent with mass degeneracy or all irreducible symmetric spaces. The solutions always correspond to a specific group coset space and are compared to the conditions for the existence of massless particles (Goldstone bosons, chiral fermions). We also discuss, on more general grounds, the possible choices of the superpotential and the appropriate holomorphic coordinates leading both to zero cosmological constant and mass degeneracy. Starting from their realization in models with flat potentials - in particular the SU( n,1)/U( n) ones - a general characterization is attempted. In this context, non-compact global symmetries of the whole Kähler potential emerge as a useful framework.