Comparison geometry referred to warped product models

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概要

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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.

• 東北大学の論文

著者

• Mashiko Yukihiro

  Department Mathematics Faculty Of Science And Engineeringa Saga University

• Mashiko Yukihiro

  Department Mathematics Faculty Of Science And Engineering Saga University

• Shiohama Katsuhiro

  Department Mathematics Faculty Of Science And Engineeringa Saga University

関連論文

• Conformally flat 3-manifolds with constant scalar curvature II
• Conformally flat 3-manifolds with constant scalar curvature
• Erratum to "Conformally flat 3-manifolds with constant scalar curvature"
• THE AXIOM OF PLANE ON WARPED PRODUCT MODELS AND ITS APPLICATION
• Comparison theorems for Riemannian manifolds with radial curvature bounded below
• Pinching theorem for the real projective space
• The isometry groups of manifolds admitting nonconstant convex functions
• Comparison geometry referred to warped product models
• An extension of a theorem of Myers
• The asymptotic cones of manifolds of roughly non-negative radial curvature
• A general rigidity theorem for complete submanifolds
• Locally convex sets in nonnegatively curved manifolds
• Riemannian manifolds with positive radial curvature

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