Unified Geometric Theory of Gravity and Supergravity

A unified geometric formulation of gravitation and supergravity is presented. The action for these theories is constructed out of the components of the curvature tensor for bundle spaces with four-dimensional Lorentz base manifold and structure groups Sp(4) for gravity and OSp(1,4) for supergravity. The requirement of invariance under reflections, local Lorentz transformations, and general coordinate transformations uniquely determines the action and ensures the existence of local supersymmetry in supergravity.