Tohoku Mathematical Journal
2006

December
SECOND SERIES VOL. 58, NO. 4

Tohoku Math. J.
58 (2006), 461-473

Title COMPARISON GEOMETRY REFERRED TO WARPED PRODUCT MODELS

Author Yukihiro Mashiko and Katsuhiro Shiohama

(Received April 16, 2004, revised June 16, 2006)
Abstract. We generalize the Alexandrov-Toponogov comparison theorem to the case of complete Riemannian manifolds referred to warped product models. We prove the maximal diameter theorem and the rigidity theorem. In particular, we discuss collapsing phenomena where the curvature explosion may occur.

2000 Mathematics Subject Classification. Primary 53C20.

Key words and phrases. Riemannian manifolds, geodesics, radial sectional curvature, Hausdorff convergence.

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