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THE MANIFOLD OF METRICS WITH A FIXED VOLUME FORM

We study the manifold of all metrics with the xed volume form on a compact Riemannian manifold of dimension 3. We compute the char- acteristic function for the L 2 (Ebin) distance to the reference metric. In the Appendix, we study Lipschitz-type distance between Riemannian metrics, and give applications to the diameter and eigenvalue functionals.