Constraints on spacetime manifold in Euclidean supergravity in terms of   Dirac eigenvalues
  We generalize previous work on Dirac eigenvalues as dynamical variables of Euclidean supergravity. The most general set of constraints on the curvatures of the tangent bundle and on the spinor bundle of the spacetime manifold under which spacetime admits Dirac eigenvalues as observables, are derived. 
C. Ciuhu and I. V. Vancea