## Tohoku Mathematical Journal

### Comparison geometry referred to warped product models

#### 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.

#### Article information

Source
Tohoku Math. J. (2), Volume 58, Number 4 (2006), 461-473.

Dates
First available in Project Euclid: 1 February 2007

https://projecteuclid.org/euclid.tmj/1170347684

Digital Object Identifier
doi:10.2748/tmj/1170347684

Mathematical Reviews number (MathSciNet)
MR2297194

Zentralblatt MATH identifier
1135.53023

#### Citation

Mashiko, Yukihiro; Shiohama, Katsuhiro. Comparison geometry referred to warped product models. Tohoku Math. J. (2) 58 (2006), no. 4, 461--473. doi:10.2748/tmj/1170347684. https://projecteuclid.org/euclid.tmj/1170347684

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