History and Development of Sphere Theorems in Riemannian Geometry

리만기하학에서 구면정리의 발전과 역사

  • Cho, Min-Shik (Department of Mathematics Education, Korea National University of Education)
  • 조민식 (한국교원대학교 수학교육과)
  • Received : 2011.06.27
  • Accepted : 2011.08.22
  • Published : 2011.08.31

Abstract

The sphere theorem is one of the main streams in modern Riemannian geometry. In this article, we survey developments of pinching theorems from the classical one to the recent differentiable pinching theorem. Also we include sphere theorems of metric invariants such as diameter and radius with historical view point.

본 논문에서는 어떤 기하학적 양이 핀치되어 있으면 위상적 또는 미분위상적인 구면이 된다는 구면정리의 발전과 역사를 다루었다. 단면곡률의 핀칭과 관련하여, 고전적 핀칭 구면 정리에서 최근에 증명된 기념비적인 미분 핀칭 구면정리로 발전하는 과정의 역사를 기술하였다. 또 직경, 반경, 부피 등과 관련하여 계량불변량 구면정리와 미분 계량불변량 구면정리의 발전의 과정을 소개하였고, 구면정리와 관련된 미해결문제에 대한 역사를 기술하였다.

Keywords

Acknowledgement

Supported by : 한국교원대학교

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