ALTERNATIVE ACTIONS FOR QUANTUM-GRAVITY AND INTRINSIC RIGIDITY OF SPACE-TIME

We generalize the Regge action of simplicial quantum gravity by ascrib ing deficit angles to the vertices of four-dimensional simplicial mani folds. The new terms suppress vertices with deficit angles different f rom zero and introduce in this way so-called intrinsic rigidity in sim plicial quantum gravity. The concept of generalized deficit angles app ear in a natural way in the Steiner-Weyl expansion formula for paralle l 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 vario us dimensions. These invariants are natural candidates for discretized actions for higher dimensional membranes.