Generalized space forms

Neil N. Katz; Kei Kondo

doi:10.1090/S0002-9947-02-02966-5

Generalized space forms

Neil N. Katz, Kei Kondo

Research output: Contribution to journal › Article › peer-review

19 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 language	English
Pages (from-to)	2279-2284
Number of pages	6
Journal	Transactions of the American Mathematical Society
Volume	354
Issue number	6
DOIs	https://doi.org/10.1090/S0002-9947-02-02966-5
Publication status	Published - 2002
Externally published	Yes

Keywords

Radial curvature
Rigidity

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9947-02-02966-5

Cite this

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title = "Generalized space forms",

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.",

keywords = "Radial curvature, Rigidity",

author = "Katz, {Neil N.} and Kei Kondo",

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doi = "10.1090/S0002-9947-02-02966-5",

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AU - Kondo, Kei

PY - 2002

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AB - 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.

KW - Radial curvature

KW - Rigidity

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ER -

Generalized space forms

Abstract

Keywords

ASJC Scopus subject areas

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