The cut loci and the conjugate loci on ellipsoids (Q1882773)

In this interesting paper the authors investigate the cut and conjugate loci of a non-umbilic point on a general ellipsoid. Their results confirm recent experimental work: they prove that the cut locus is a subarc of one of the curvature lines passing through the antipodal point, cf. [the first author and \textit{R. Sinclair}, Exp. Math. 13, No. 3, 309--325 (2004)], and that the conjugate locus has four cusps, a statement attributed to C. Jacobi [cf. \textit{R. Sinclair}, Exp. Math. 12, 477--485 (2003; Zbl 1073.53007)].