The Cut Loci on Ellipsoids and Certain Liouville Manifolds

We show that some riemannian manifolds diffeomorphic to the sphere have the property that the cut loci of general points are smoothly embedded closed disks of codimension one. Ellipsoids with distinct axes are typical examples of such manifolds.

Keywords

Cut locus, ellipsoid, Liouville manifold, integrable geodesic flow

2010 Mathematics Subject Classification

Primary 53C22. Secondary 53A05.

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Published 1 January 2010