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.
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Itoh, Ji., Kiyohara, K. Cut loci and conjugate loci on Liouville surfaces. manuscripta math. 136, 115–141 (2011). https://doi.org/10.1007/s00229-011-0433-1
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DOI: https://doi.org/10.1007/s00229-011-0433-1