We determine the structure of the cut locus of a class of two-spheres of revolution, which includes all ellipsoids of revolution. Furthermore, we show that a subclass of this class gives a new model surface for Toponogov's comparison theorem.
Publié le : 2007-05-14
Classification:
Cut locus,
Toponogov's comparison theorem,
ellipsoid of revolution,
geodesic,
53C22
@article{1192117984,
author = {Sinclair, Robert and Tanaka, Minoru},
title = {The cut locus of a two-sphere of revolution and Toponogov's comparison theorem},
journal = {Tohoku Math. J. (2)},
volume = {59},
number = {1},
year = {2007},
pages = { 379-399},
language = {en},
url = {http://dml.mathdoc.fr/item/1192117984}
}
Sinclair, Robert; Tanaka, Minoru. The cut locus of a two-sphere of revolution and Toponogov's comparison theorem. Tohoku Math. J. (2), Tome 59 (2007) no. 1, pp. 379-399. http://gdmltest.u-ga.fr/item/1192117984/