The cut loci and the conjugate loci on ellipsoids

Jin Ichi Itoh; Kazuyoshi Kiyohara

doi:10.1007/s00229-004-0455-z

The cut loci and the conjugate loci on ellipsoids

Jin Ichi Itoh, Kazuyoshi Kiyohara

Research output: Contribution to journal › Article › peer-review

36 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	247-264
Number of pages	18
Journal	Manuscripta Mathematica
Volume	114
Issue number	2
DOIs	https://doi.org/10.1007/s00229-004-0455-z
Publication status	Published - Jun 2004

ASJC Scopus subject areas

Mathematics(all)

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abstract = "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.",

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AU - Itoh, Jin Ichi

AU - Kiyohara, Kazuyoshi

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The cut loci and the conjugate loci on ellipsoids

Abstract

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