COMPARISON GEOMETRY REFERRED TO WARPED PRODUCT MODELS

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Author(s)

    • MASHIKO YUKIHIRO
    • Department of Mathematics, Faculty of Science and Engineering, Saga University

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.

Journal

  • Tohoku Mathematical Journal, Second Series

    Tohoku Mathematical Journal, Second Series 58(4), 461-473, 2006

    Tohoku University

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