| Abstract: | The Fréchet manifold E/ ~ {cal E}/_{!sim} of all embeddings (up to orientation preserving reparametrizations) of the circle in S 3 has a canonical weak Riemannian metric. We use the characterization obtained by H. Gluck and F. Warner of the oriented great circle fibrations of S 3 to prove that among all such fibrations π:S 3→B, the manifold B consisting of the oriented fibers is totally geodesic in E/ ~ {cal E}/_{sim } , or has minimum volume or diameter with the induced metric, exactly when π is a Hopf fibration. |
