The cut loci and the conjugate loci on ellipsoids

Jin Ichi Itoh, Kazuyoshi Kiyohara

Research output: Contribution to journalArticlepeer-review

36 Citations (Scopus)


We prove that the cut locus of any point on any ellipsoid is an arc on the curvature line through the antipodal point. Also, we prove that the conjugate locus has exactly four cusps, which is known as the last geometric statement of Jacobi.

Original languageEnglish
Pages (from-to)247-264
Number of pages18
JournalManuscripta Mathematica
Issue number2
Publication statusPublished - Jun 2004

ASJC Scopus subject areas

  • Mathematics(all)


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