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.
|Number of pages||27|
|Publication status||Published - Sept 2011|
- Primary 53C22
- Secondary 53A05
ASJC Scopus subject areas