대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제20권2호
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  • Pages.195-207
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  • 2005
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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양의 단면 곡률을 가지는 컴팩트 공간에 대하여

  • 고관석 (인하대학교 이과대학 수학통계학부)
  • 발행 : 2005.04.01
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⟨ 이전 논문 다음 논문 ⟩

초록

리만 기하학에서 중요한 문제중의 하나는 주어진 곡률부호를 가지는 다양체를 분류하는 것이다. 그렇게 하기 위해서는 곡률과 위상과의 상호 관계를 밝히는 것이 중요하다. 특히 양의 곡률을 가지는 공간을 분류하는 것은 어려운 문제로 알려져 있으며 위상적 성질에 대해서도 알려진 것은 매우 적다. 본 논문에서는 지금까지 알려진 양의 곡률을 가지는 공간들을 살펴 보고 그들 공간들에 대한 일반적인 정리들과 호프의 문제를 소개하고자 한다.

키워드

참고문헌

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