manuscripta mathematica

, Volume 114, Issue 2, pp 247–264

The cut loci and the conjugate loci on ellipsoids

Article

DOI: 10.1007/s00229-004-0455-z

Cite this article as:
Itoh, J. & Kiyohara, K. manuscripta math. (2004) 114: 247. doi:10.1007/s00229-004-0455-z

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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of MathematicsFaculty of Education, Kumamoto UniversityKumamotoJapan
  2. 2.Department of MathematicsFaculty of Science, Okayama UniversityOkayamaJapan