Tohoku Mathematical Journal
2007

September
SECOND SERIES VOL. 59, NO. 3

Tohoku Math. J.
59 (2007), 379-399

Title THE CUT LOCUS OF A TWO-SPHERE OF REVOLUTION AND TOPONOGOV'S COMPARISON THEOREM

Author Robert Sinclair and Minoru Tanaka

(Received February 13, 2006, revised November 10, 2006)
Abstract. 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.

2000 Mathematics Subject Classification. Primary 53C22.

Key words and phrases. Cut locus, Toponogov's comparison theorem, ellipsoid of revolution, geodesic.

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