Antipodal Points and Diameter of a Sphere
Received 04 November 2018
2018, Vol. 14, no. 4, pp. 579-581
Author(s): Podobryaev A.
We give an example of a Riemannian manifold homeomorphic to a sphere such that its diameter cannot be realized as a distance between antipodal points. We consider a Berger sphere, i.e., a three-dimensional sphere with Riemannian metric that is compressed along the fibers of the Hopf fibration. We give a condition for a Berger sphere to have the desired property. We use our previous results on a cut locus of Berger spheres obtained by the method from geometric control theory.
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