Cut loci and conjugate loci on Liouville surfaces

Jin ichi Itoh, Kazuyoshi Kiyohara

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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 show that 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.

Original languageEnglish
Pages (from-to)115-141
Number of pages27
JournalManuscripta Mathematica
Issue number1
Publication statusPublished - Sept 2011
Externally publishedYes


  • Primary 53C22
  • Secondary 53A05

ASJC Scopus subject areas

  • Mathematics(all)


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