The Blaschke Conjecture and Great Circle Fibrations of Spheres

We construct an explicit diffeomorphism taking any fibration of a sphere by great circles into the Hopf fibration. We use elementary differential geometry, and no surgery or K-theory, to carry out the construction—indeed the diffeomorphism is a local (differential) invariant, algebraic in derivatives. This result is new only for 5 dimensional spheres, but… CONTINUE READING