Alternative actions for quantum gravity and intrinsic rigidity of space-time

We generalize the Regge action of simplicial quantum gravity by ascribing deficit angles to the vertices of four-dimensional simplicial manifolds. The new terms suppress vertices with deficit angles different from zero and introduce in this way so-called intrinsic rigidity in simplicial quantum gravity. The concept of generalized deficit angles appear in a natural way in the Steiner-Weyl expansion formula for parallel manifolds and is related to higher order curvature terms, We discuss the concept of rigidity in quantum gravity and its relation to the so-called goni-hedric principle, This principle allows us to End a large class of integral invariants defined on simplicial manifolds of various dimensions. These invariants are natural candidates for discretized actions for higher dimensional membranes.