Springer Acta Medica Okayama 0025-2611 136 1-2 2011 Cut loci and conjugate loci on Liouville surfaces 115 141 EN Jin-ichi Itoh Kazuyoshi Kiyohara In the earlier paper (Itoh and Kiyohara, Manuscr Math 114:247–264, 2004), we showed that the cut locus of a general point on two-dimensional ellipsoid is a segment of a curvature line and proved "Jacobi’s last geometric statement" on the singularities of the conjugate locus. In the present paper,we showthat a wider class of Liouville surfaces possess such simple cut loci and conjugate loci. The results include the determination of cut loci and the set of poles on two-sheeted hyperboloids and elliptic paraboloids. No potential conflict of interest relevant to this article was reported.

Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 47 1 2005 Appendix to "Some Metric Invariants of Spheres and Alexandrov Spaces II'' 189 192 EN Kazuyoshi Kiyohara 10.18926/mjou/33595 No potential conflict of interest relevant to this article was reported.