CHAPTER III

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 ...

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