Comparison geometry referred to warped product models
Mashiko, Yukihiro ; Shiohama, Katsuhiro
Tohoku Math. J. (2), Tome 58 (2006) no. 1, p. 461-473 / Harvested from Project Euclid
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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.
Publié le : 2006-12-14
Classification:  Riemannian manifolds,  geodesics,  radial sectional curvature,  Hausdorff convergence,  53C20 
@article{1170347684,
     author = {Mashiko, Yukihiro and Shiohama, Katsuhiro},
     title = {Comparison geometry referred to warped product models},
     journal = {Tohoku Math. J. (2)},
     volume = {58},
     number = {1},
     year = {2006},
     pages = { 461-473},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1170347684}
}

Mashiko, Yukihiro; Shiohama, Katsuhiro. Comparison geometry referred to warped product models. Tohoku Math. J. (2), Tome 58 (2006) no. 1, pp.  461-473. http://gdmltest.u-ga.fr/item/1170347684/