To build the Kaluza–Klein theory, one picks an invariant metric on the circle S 1 that is the fiber of the U(1)-bundle of electromagnetism. In this discussion, an invariant metric is simply one that is invariant under rotations of the circle. Suppose that this metric gives the circle a total length Λ Λ . One then considers metrics g ^ ^ on the bundle P that are consistent with both the fiber metric, and the metric on the underlying manifold M . The consistency conditions are: