The cut loci and the conjugate loci on ellipsoids
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- Itoh, J. & Kiyohara, K. manuscripta math. (2004) 114: 247. doi:10.1007/s00229-004-0455-z
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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.