SYMMETRIC SPACES OF RANK ONE
1. Flat tori
Let (X, g) be a flat Riemannian manifold of dimension n. We first suppose that X is the circle S1 of length endowed with the Riemannian metric where t is the canonical coordinate of S1 defined modulo L. It is easily seen that this space X is infinitesimally rigid and that a 1-form on X satisfies the zero-energy condition if and only if it is exact.
In this section, we henceforth suppose that n 2. We recall that that the operator D1 is equal to Dg, and that the sequence (1.50) is exact. Let ...