Tanaka, Minoru A differentiable point of the distance function to the cut locus. (English) Zbl 1017.53040 Proc. Sch. Sci. Tokai Univ. 37, 19-21 (2002). In this note, the author announces a characterization of the points in the unit normal bundle of a closed submanifold \(N\) in a 2-dimensional complete Riemannian manifold \(M\) where the distance function \(\rho\) to the cut locus of \(N\) is differentiable. This result is motivated by a conjecture due to S. L. Kokkendorff, that was in turn inspired by the experimentation with the software tool “Loki”. Reviewer: Vicente Palmer (Castello) MSC: 53C22 Geodesics in global differential geometry Keywords:closed submanifold; geodesic segment; cut locus; distance function; submanifold; software tool “Loki” Software:Loki PDFBibTeX XMLCite \textit{M. Tanaka}, Proc. Sch. Sci. Tokai Univ. 37, 19--21 (2002; Zbl 1017.53040)