COMPARISON GEOMETRY REFERRED TO WARPED PRODUCT MODELS
2006 年 58 巻 4 号 p. 461-473
詳細
2006 年 58 巻 4 号 p. 461-473
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.
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