Resumen de Some Geometric Characterizations of the Hopf Fibrations of the Three-Sphere

Marcos Salvai

• The Fréchet 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