Abstract
The Frechet manifold 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 p:S 3?B, the manifold B consisting of the oriented fibers is totally geodesic in , or has minimum volume or diameter with the induced metric, exactly when p is a Hopf fibration
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