Generalized space forms

Neil N. Katz, Kei Kondo

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)

Abstract

Spaces with radially symmetric curvature at base point p are shown to be diffeomorphic to space forms. Furthermore, they are either isometric to ℝn or Sn under a radially symmetric metric, to ℝPn with Riemannian universal covering of Sn equipped with a radially symmetric metric, or else have constant curvature outside a metric ball of radius equal to the injectivity radius at p.

Original languageEnglish
Pages (from-to)2279-2284
Number of pages6
JournalTransactions of the American Mathematical Society
Volume354
Issue number6
DOIs
Publication statusPublished - 2002
Externally publishedYes

Keywords

  • Radial curvature
  • Rigidity

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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