start-ver=1.4 cd-journal=joma no-vol=136 cd-vols= no-issue=1-2 article-no= start-page=115 end-page=141 dt-received= dt-revised= dt-accepted= dt-pub-year=2011 dt-pub=201109 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=Cut loci and conjugate loci on Liouville surfaces en-subtitle= kn-subtitle= en-abstract= kn-abstract=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. en-copyright= kn-copyright= en-aut-name=ItohJin-ichi en-aut-sei=Itoh en-aut-mei=Jin-ichi kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= en-aut-name=KiyoharaKazuyoshi en-aut-sei=Kiyohara en-aut-mei=Kazuyoshi kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=2 ORCID= affil-num=1 en-affil= kn-affil=Department of Mathematics, Faculty of Education, Kumamoto University affil-num=2 en-affil= kn-affil=Department of Mathematics, Faculty of Science, Okayama University END