Geometrical Constraints on the Cosmological Constant

The cosmological constant problem is examined under the assumption that the extrinsic curvature of the space-time contributes to the vacuum. A compensation mechanism based on a variable cosmological term is proposed. Under a suitable hypothesis on the behavior of the extrinsic curvature, we find that an initially large $\mathrm{\Lambda }(t)$ rolls down rapidly to zero during the early stages of the universe. Using perturbation analysis, it is shown that such vacuum behaves essentially as a spin-2 field which is independent of the metric.