Geodesic
Antipodal Points and Diameter of a Sphere
Russian journal of nonlinear dynamics, Tome 14 (2018) no. 4, pp. 579-581

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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.
Keywords: diameter, Berger sphere, cut locus, geometric control theory.
Mots-clés : $SU_2$, antipodal points 
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     author = {A. V. Podobryaev},
     title = {Antipodal {Points} and {Diameter} of a {Sphere}},
     journal = {Russian journal of nonlinear dynamics},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ND_2018_14_4_a9/}
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A. V. Podobryaev. Antipodal Points and Diameter of a Sphere. Russian journal of nonlinear dynamics, Tome 14 (2018) no. 4, pp. 579-581. http://geodesic.mathdoc.fr/item/ND_2018_14_4_a9/