Cut loci and conjugate loci on Liouville surfaces

Jin ichi Itoh, Kazuyoshi Kiyohara

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 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
Volume136
Issue number1
DOIs
Publication statusPublished - Sep 2011

Fingerprint

Cut Locus
Locus
Ellipsoid
Jacobi
Pole
Curvature
Singularity
Line

Keywords

  • Primary 53C22
  • Secondary 53A05

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Cut loci and conjugate loci on Liouville surfaces. / Itoh, Jin ichi; Kiyohara, Kazuyoshi.

In: Manuscripta Mathematica, Vol. 136, No. 1, 09.2011, p. 115-141.

Research output: Contribution to journalArticle

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