The existence of nontriangulable cut loci
David A. Singer, Herman Gluck · Bulletin of the American Mathematical Society · 1976
We continue in this note the description of deformation theorems for geodesic fields on a Riemannian manifold begun in [1], restricting ourselves here to surfaces of revolution and to deformations of metric within this class.Using real and holomorphic Fourier transforms, we obtain in Theorem 2 an explicit formula for the deformation of metric corresponding to a prescribed deflection of geodesies.As an application, we turn again to the structure of the cut locus and prove THEOREM 1.There exists in R 3 a strictly convex surface of revolution containing a nonempty open set of points p for which the cut locus C(p) is nontriangulable.