Differentiable sphere theorems whose comparison spaces are standard spheres or exotic ones

Kei Kondo, Minoru Tanaka

Research output: Contribution to journalArticlepeer-review

Abstract

We show that for an arbitrarily given closed Riemannian manifold M admitting a point p ∊ M with a single cut point, every closed Riemannian manifold N admitting a point q ∊ N with a single cut point is diffeomorphic to M if the radial curvatures of N at q are sufficiently close in the sense of L1-norm to those of M at p.

Original languageEnglish
Pages (from-to)349-365
Number of pages17
JournalKodai Mathematical Journal
Volume43
Issue number2
DOIs
Publication statusPublished - 2020

Keywords

  • Bi-Lipschitz homeomorphism
  • Differentiable sphere theorem
  • Exotic spheres
  • Radial curvature
  • The Blaschke conjecture for spheres
  • The Cartan-Ambrose-Hicks theorem

ASJC Scopus subject areas

  • Mathematics(all)

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